def check_ideal_labels(field_label='2.2.5.1', min_norm=0, max_norm=None, fix=False, verbose=False):
r""" Go through all curves with the given field label, assumed totally
real, check whether the ideal label agrees with the level_label of
the associated Hilbert Modular Form.
"""
hmfs = conn.hmfs
forms = hmfs.forms
fields = hmfs.fields
query = {}
query['field_label'] = field_label
query['conductor_norm'] = {'$gte' : int(min_norm)}
if max_norm:
query['conductor_norm']['$lte'] = int(max_norm)
else:
max_norm = 'infinity'
cursor = nfcurves.find(query)
nfound = 0
nnotfound = 0
K = HilbertNumberField(field_label)
# NB We used to have 20 in the next line but that is insufficient
# to distinguish the a_p for forms 2.2.12.1-150.1-a and
# 2.2.12.1-150.1-b !
primes = [P['ideal'] for P in K.primes_iter(30)]
remap = {} # remap[old_label] = new_label
for ec in cursor:
fix_needed = False
cond_label = ec['conductor_label']
if cond_label in remap:
new_cond_label = remap[cond_label]
fix_needed=(cond_label!=new_cond_label)
if not fix_needed:
if verbose:
print("conductor label %s ok" % cond_label)
else:
conductor = make_conductor(ec,K)
level = K.ideal(cond_label)
new_cond_label = K.ideal_label(conductor)
remap[cond_label] = new_cond_label
fix_needed=(cond_label!=new_cond_label)
if fix_needed:
print("conductor label for curve %s is wrong, should be %s not %s" % (ec['label'],new_cond_label, cond_label))
if fix:
iso = ec['iso_label']
num = str(ec['number'])
newlabeldata = {}
newlabeldata['conductor_label'] = new_cond_label
newlabeldata['short_class_label'] = '-'.join([new_cond_label,iso])
newlabeldata['short_label'] = ''.join([newlabeldata['short_class_label'],num])
newlabeldata['class_label'] = '-'.join([field_label,
newlabeldata['short_class_label']])
newlabeldata['label'] = '-'.join([field_label,
newlabeldata['short_label']])
nfcurves.update({'_id': ec['_id']}, {"$set": newlabeldata}, upsert=True)
else:
if verbose:
print("conductor label %s ok" % cond_label)
return dict([(k,remap[k]) for k in remap if not k==remap[k]])
def compare_with_db(self, field=None):
lab = self.dbdata['label']
f = WebHMF.by_label(lab)
if f==None:
print("No Hilbert newform in the database has label %s" % lab)
return False
if field==None:
field = HilbertNumberField(self.dbdata['field_label'])
agree = True
for key in self.dbdata.keys():
if key in ['is_base_change', 'is_CM']:
continue
if key=='hecke_eigenvalues':
if self.dbdata[key]!=f.dbdata[key]:
agree = False
print("Inconsistent data for HMF %s in field %s" % (lab,key))
print("self has %s entries, \ndb has %s entries" % (len(self.dbdata[key]),len(f.dbdata[key])))
print("Entries differ at indices %s" % [i for i in range(len(self.dbdata[key])) if self.dbdata[key][i]!=f.dbdata[key][i]])
elif key=='level_ideal':
if self.dbdata[key]!=f.dbdata[key]:
I = field.ideal_from_str(f.dbdata['level_ideal'])[2]
J = field.ideal_from_str(self.dbdata['level_ideal'])[2]
if I==J:
print("OK, these are the same ideal")
else:
agree = False
print("These are different ideals!")
else:
if self.dbdata[key]!=f.dbdata[key]:
agree = False
print("Inconsistent data for HMF %s in field %s" % (lab,key))
return agree
def magma_output_iter(infilename):
r"""
Read Magma search output, as an iterator yielding the curves found.
INPUT:
- ``infilename`` (string) -- name of file containing Magma output
"""
infile = file(infilename)
while True:
try:
L = infile.next()
except StopIteration:
raise StopIteration
if 'Field' in L:
field_label = L.split()[1]
K = HilbertNumberField(field_label)
KK = K.K()
if 'Isogeny class' in L:
class_label = L.split()[2]
cond_label, iso_label = class_label.split("-")
num = 0
if 'Conductor' in L:
cond_ideal = L.replace("Conductor ", "")
if 'Curve' in L:
ai = [KK(a.encode()) for a in L[7:-2].split(",")]
num += 1
yield field_label, cond_label, iso_label, num, cond_ideal, ai
infile.close()
def check_ideal_labels(field_label='2.2.5.1', min_norm=0, max_norm=None, fix=False, verbose=False):
r""" Go through all curves with the given field label, assumed totally
real, check whether the ideal label agrees with the level_label of
the associated Hilbert Modular Form.
"""
hmfs = conn.hmfs
forms = hmfs.forms
fields = hmfs.fields
query = {}
query['field_label'] = field_label
query['conductor_norm'] = {'$gte': int(min_norm)}
if max_norm:
query['conductor_norm']['$lte'] = int(max_norm)
else:
max_norm = 'infinity'
cursor = nfcurves.find(query)
nfound = 0
nnotfound = 0
K = HilbertNumberField(field_label)
# NB We used to have 20 in the next line but that is insufficient
# to distinguish the a_p for forms 2.2.12.1-150.1-a and
# 2.2.12.1-150.1-b !
primes = [P['ideal'] for P in K.primes_iter(30)]
remap = {} # remap[old_label] = new_label
for ec in cursor:
fix_needed = False
cond_label = ec['conductor_label']
if cond_label in remap:
new_cond_label = remap[cond_label]
fix_needed = (cond_label != new_cond_label)
if not fix_needed:
if verbose:
print("conductor label %s ok" % cond_label)
else:
conductor = make_conductor(ec, K)
level = K.ideal(cond_label)
new_cond_label = K.ideal_label(conductor)
remap[cond_label] = new_cond_label
fix_needed = (cond_label != new_cond_label)
if fix_needed:
print("conductor label for curve %s is wrong, should be %s not %s" % (ec['label'], new_cond_label, cond_label))
if fix:
iso = ec['iso_label']
num = str(ec['number'])
newlabeldata = {}
newlabeldata['conductor_label'] = new_cond_label
newlabeldata['short_class_label'] = '-'.join([new_cond_label, iso])
newlabeldata['short_label'] = ''.join([newlabeldata['short_class_label'], num])
newlabeldata['class_label'] = '-'.join([field_label,
newlabeldata['short_class_label']])
newlabeldata['label'] = '-'.join([field_label,
newlabeldata['short_label']])
nfcurves.update({'_id': ec['_id']}, {"$set": newlabeldata}, upsert=True)
else:
if verbose:
print("conductor label %s ok" % cond_label)
return dict([(k, remap[k]) for k in remap if not k == remap[k]])
def check_multiplicity_one(label):
F = HilbertNumberField(label)
count = 0
for N in F.ideals_iter():
Lf = forms.find({'field_label':label, 'level_label':N['label']})
Lf = [f for f in Lf]
n = len(Lf)
for i in range(n):
for j in range(i+1,n):
if forms_equal(Lf[i],Lf[j]):
count += 1
print "duplicates: "+Lf[i]['label']+" and "+Lf[j]['label']
print("Found "+str(count)+" duplicate forms.")
def check_multiplicity_one(label):
F = HilbertNumberField(label)
count = 0
for N in F.ideals_iter():
Lf = forms.find({'field_label':label, 'level_label':N['label']})
Lf = [f for f in Lf]
n = len(Lf)
for i in range(n):
for j in range(i+1,n):
if forms_equal(Lf[i],Lf[j]):
count += 1
print("duplicates: "+Lf[i]['label']+" and "+Lf[j]['label'])
print("Found "+str(count)+" duplicate forms.")
def checkprimes(label):
Fdata = get_Fdata(label)
gen_name = findvar(Fdata['ideals'])
WebF = get_WNF(label, gen_name)
F = WebF.K()
ideals = niceideals(F, Fdata['ideals'])
primes = niceideals(F, Fdata['primes'])
F = HilbertNumberField(label)
L = []
for prhnf, prideal, prlabel in primes:
ideal = F.ideal(prlabel)
if ideal != prideal:
L.append(prlabel)
return L
def checkprimes(label):
Fdata = get_Fdata(label)
gen_name = findvar(Fdata['ideals'])
WebF = get_WNF(label, gen_name)
F = WebF.K()
# ideals = niceideals(F, Fdata['ideals']) # never used
primes = niceideals(F, Fdata['primes'])
F = HilbertNumberField(label)
L = []
for prhnf,prideal,prlabel in primes:
ideal = F.ideal(prlabel)
if ideal != prideal:
L.append(prlabel)
return L
def export_magma_output(infilename, outfilename=None, verbose=False):
r"""
Convert Magma search output to a curves file.
INPUT:
- ``infilename`` (string) -- name of file containing Magma output
- ``outfilename`` (string, default ``None``) -- name of output file
- ``verbose`` (boolean, default ``False``) -- verbosity flag.
"""
if outfilename:
outfile = file(outfilename, mode="w")
def output(L):
if outfilename:
outfile.write(L)
if verbose:
sys.stdout.write(L)
K = None
for field_label, cond_label, iso_label, num, cond_ideal, ai in magma_output_iter(
infilename):
ec = {}
ec['field_label'] = field_label
if not K:
K = HilbertNumberField(field_label)
ec['conductor_label'] = cond_label
ec['iso_label'] = iso_label
ec['number'] = num
N = K.ideal(cond_label)
norm = N.norm()
hnf = N.pari_hnf()
ec['conductor_ideal'] = cond_ideal
ec['conductor_ideal'] = "[%i,%s,%s]" % (norm, hnf[1][0], hnf[1][1])
ec['conductor_norm'] = norm
ec['ainvs'] = [[str(c) for c in list(a)] for a in ai]
ec['cm'] = '?'
ec['base_change'] = []
output(make_curves_line(ec) + "\n")
def export_magma_output(infilename, outfilename=None, verbose=False):
r"""
Convert Magma search output to a curves file.
INPUT:
- ``infilename`` (string) -- name of file containing Magma output
- ``outfilename`` (string, default ``None``) -- name of output file
- ``verbose`` (boolean, default ``False``) -- verbosity flag.
"""
if outfilename:
outfile = file(outfilename, mode="w")
def output(L):
if outfilename:
outfile.write(L)
if verbose:
sys.stdout.write(L)
K = None
for field_label, cond_label, iso_label, num, cond_ideal, ai in magma_output_iter(infilename):
ec = {}
ec['field_label'] = field_label
if not K:
K = HilbertNumberField(field_label)
ec['conductor_label'] = cond_label
ec['iso_label'] = iso_label
ec['number'] = num
N = K.ideal(cond_label)
norm = N.norm()
hnf = N.pari_hnf()
ec['conductor_ideal'] = cond_ideal
ec['conductor_ideal'] = "[%i,%s,%s]" % (norm, hnf[1][0], hnf[1][1])
ec['conductor_norm'] = norm
ec['ainvs'] = [[str(c) for c in list(a)] for a in ai]
ec['cm'] = '?'
ec['base_change'] = []
output(make_curves_line(ec) + "\n")
def create_from_data_string(self, label_or_field, L):
"""Takes an input line L from a raw data file and constructs the
associated HMF object with given base field.
String sample:
<[31, 31, w + 12], "a", [-3, -2, 2, 4, -4, ...]>,
"""
data = self.dbdata = {}
if isinstance(label_or_field, str):
label = label_or_field
data['field_label'] = label
F = HilbertNumberField(label)
if not F:
raise ValueError("No Hilbert number field with label %s is in the database" % label)
elif label_or_field == None:
raise ValueError("Must specify a valid field label")
else: # we were passed a HilbertNumberField already
F = label_or_field
data['field_label'] = F.label
#print("data['field_label'] = %s" % data['field_label'])
# The level
i = L.find('[')
j = L.find(']')
data['level_ideal'] = L[i:j+1]
#print("data['level_ideal'] = %s" % data['level_ideal'])
N, n, alpha = data['level_ideal'][1:-1].split(',')
data['level_norm'] = int(N)
#print("data['level_norm'] = %s" % data['level_norm'])
level = F.ideal_from_str(data['level_ideal'])[2]
#print("level = %s" % level)
data['level_label'] = F.ideal_label(level)
#print("data['level_label'] = %s" % data['level_label'])
# The weight
data['parallel_weight'] = int(2)
data['weight'] = str([data['parallel_weight']] * F.degree())
weight = [2] * F.degree()
# The label
i = L.find('"')
j = L.find('"', i+1)
data['label_suffix'] = L[i+1:j].replace(" ","")
data['label'] = construct_full_label(data['field_label'],
weight,
data['level_label'],
data['label_suffix'])
data['short_label'] = '-'.join([data['level_label'], data['label_suffix']])
#print("data['label'] = %s" % data['label'] )
#print("data['short_label'] = %s" % data['short_label'] )
# The hecke polynomial and degree
if 'x' in L:
# non-rational
i = L.find("x")
j = L.find(i+1,",")
data['hecke_polynomial'] = pol = L[i:j]
data['dimension'] = int(1)
x = polygen(QQ)
hpol = x.parent()(str(pol))
data['dimension'] = int(hpol.degree())
else:
# rational
data['hecke_polynomial'] = 'x'
data['dimension'] = int(1)
i = L.rfind("[")
j = L.rfind("]")
data['hecke_eigenvalues'] = L[i+1:j].replace(" ","").split(",")
data['hecke_eigenvalues'] = [unicode(s) for s in data['hecke_eigenvalues']]
#print("hecke_eigenvalues = %s..." % data['hecke_eigenvalues'][:20])
# Find (some of the) AL-eigenvalues
BP = level.prime_factors()
BP_indices = [F.prime_index(P) for P in BP]
print("BP_indices = %s" % BP_indices)
BP_exponents = [level.valuation(P) for P in BP]
#print("BP_exponents = %s" % BP_exponents)
AL_eigs = [int(data['hecke_eigenvalues'][k]) for k in BP_indices]
#print("AL_eigs = %s" % AL_eigs)
if not all([(e==1 and eig in [-1,1]) or (eig==0)
for e,eig in zip(BP_exponents,AL_eigs)]):
print("Some bad AL-eigenvalues found")
# NB the following will put 0 for the eigenvalue for primes
# whose quare divides the level; this will need fixing later.
data['AL_eigenvalues'] = [[F.primes[k],data['hecke_eigenvalues'][k]] for k in BP_indices]
data['is_CM'] = '?'
data['is_base_change'] = '?'
def find_curves(field_label='2.2.5.1',
min_norm=0,
max_norm=None,
outfilename=None,
verbose=False):
r""" Go through all Hilbert Modular Forms with the given field label,
assumed totally real, for level norms in the given range, test
whether an elliptic curve exists with the same label; if not, find
the curves using Magma; output these to a file.
"""
query = {}
query['field_label'] = field_label
if fields.find({'label': field_label}).count() == 0:
if verbose:
print("No HMF data for field %s" % field_label)
return None
query['dimension'] = 1 # only look at rational newforms
query['level_norm'] = {'$gte': int(min_norm)}
if max_norm:
query['level_norm']['$lte'] = int(max_norm)
else:
max_norm = 'infinity'
cursor = forms.find(query)
nfound = 0
nnotfound = 0
nok = 0
missing_curves = []
K = HilbertNumberField(field_label)
primes = [P['ideal'] for P in K.primes_iter(100)]
curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap
form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap
# Step 1: look at all newforms, check that there is an elliptic
# curve of the same label, and if so compare ap-lists. The
# dicts curve_ap and form_ap store these when there is
# disagreement: e.g. curve_ap[conductor_label][iso_label] =
# aplist.
for f in cursor:
curve_label = f['label']
ec = nfcurves.find_one({
'field_label': field_label,
'class_label': curve_label,
'number': 1
})
if ec:
if verbose:
print("curve with label %s found in the database" %
curve_label)
nfound += 1
ainvsK = [K.K()([QQ(str(c)) for c in ai]) for ai in ec['ainvs']]
E = EllipticCurve(ainvsK)
good_flags = [E.has_good_reduction(P) for P in primes]
good_primes = [P for (P, flag) in zip(primes, good_flags) if flag]
aplist = [
E.reduction(P).trace_of_frobenius() for P in good_primes[:30]
]
f_aplist = [int(a) for a in f['hecke_eigenvalues'][:40]]
f_aplist = [ap for ap, flag in zip(f_aplist, good_flags)
if flag][:30]
if aplist == f_aplist:
nok += 1
if verbose:
print("Curve %s and newform agree!" % ec['short_label'])
else:
print("Curve %s does NOT agree with newform" %
ec['short_label'])
if verbose:
print("ap from curve: %s" % aplist)
print("ap from form: %s" % f_aplist)
if not ec['conductor_label'] in curve_ap:
curve_ap[ec['conductor_label']] = {}
form_ap[ec['conductor_label']] = {}
curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
else:
if verbose:
print("No curve with label %s found in the database!" %
curve_label)
missing_curves.append(f['short_label'])
nnotfound += 1
# Report progress:
n = nfound + nnotfound
if nnotfound:
print(
"Out of %s newforms, %s curves were found in the database and %s were not found"
% (n, nfound, nnotfound))
else:
print(
"Out of %s newforms, all %s had curves with the same label and ap"
% (n, nfound))
if nfound == nok:
print("All curves agree with matching newforms")
else:
print("%s curves agree with matching newforms, %s do not" %
(nok, nfound - nok))
if nnotfound:
print("Missing curves: %s" % missing_curves)
else:
return
# Step 2: for each newform for which there was no curve, call interface to Magma's EllipticCurveSearch()
if outfilename:
outfile = file(outfilename, mode="w")
def output(L):
if outfilename:
outfile.write(L)
if verbose:
sys.stdout.write(L)
for nf_label in missing_curves:
if verbose:
print("Curve %s is missing from the database..." % nf_label)
form = forms.find_one({
'field_label': field_label,
'short_label': nf_label
})
if not form:
print("... form %s not found!" % nf_label)
else:
if verbose:
print("... found form, calling Magma search")
N = K.ideal(form['level_label'])
Plist = [P['ideal'] for P in K.primes_iter(30)]
goodP = [(i, P) for i, P in enumerate(Plist) if not P.divides(N)]
label = form['short_label']
aplist = [int(form['hecke_eigenvalues'][i]) for i, P in goodP]
curves = EllipticCurveSearch(K.K(), Plist, N, aplist[:5])
#curves = EllipticCurveSearch(K.K(), [], N, [])
if curves:
E = curves[0]
print("%s curves found by Magma, first is %s" %
(len(curves), E))
else:
print("No curves found by Magma (using %s ap)" % len(aplist))
ec = {}
ec['field_label'] = field_label
ec['conductor_label'] = form['level_label']
ec['iso_label'] = form['label_suffix']
ec['number'] = int(1)
ec['conductor_ideal'] = form['level_ideal'].replace(" ", "")
ec['conductor_norm'] = form['level_norm']
ai = E.ainvs()
ec['ainvs'] = [[str(c) for c in list(a)] for a in ai]
ec['cm'] = '?'
ec['base_change'] = []
output(make_curves_line(ec) + "\n")
def find_curves(field_label='2.2.5.1', min_norm=0, max_norm=None, outfilename=None, verbose=False):
r""" Go through all Hilbert Modular Forms with the given field label,
assumed totally real, for level norms in the given range, test
whether an elliptic curve exists with the same label; if not, find
the curves using Magma; output these to a file.
"""
query = {}
query['field_label'] = field_label
if fields.find({'label': field_label}).count() == 0:
if verbose:
print("No HMF data for field %s" % field_label)
return None
query['dimension'] = 1 # only look at rational newforms
query['level_norm'] = {'$gte': int(min_norm)}
if max_norm:
query['level_norm']['$lte'] = int(max_norm)
else:
max_norm = 'infinity'
cursor = forms.find(query)
cursor.sort([('level_norm', pymongo.ASCENDING)])
labels = [f['label'] for f in cursor]
nfound = 0
nnotfound = 0
nok = 0
missing_curves = []
K = HilbertNumberField(field_label)
primes = [P['ideal'] for P in K.primes_iter(100)]
curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap
form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap
# Step 1: look at all newforms, check that there is an elliptic
# curve of the same label, and if so compare ap-lists. The
# dicts curve_ap and form_ap store these when there is
# disagreement: e.g. curve_ap[conductor_label][iso_label] =
# aplist.
for curve_label in labels:
# We find the forms again since otherwise the cursor might timeout during the loop.
f = forms.find_one({'label': curve_label})
ec = nfcurves.find_one({'field_label': field_label, 'class_label': curve_label, 'number': 1})
if ec:
if verbose:
print("curve with label %s found in the database" % curve_label)
nfound += 1
ainvsK = [K.K()([QQ(str(c)) for c in ai]) for ai in ec['ainvs']]
E = EllipticCurve(ainvsK)
good_flags = [E.has_good_reduction(P) for P in primes]
good_primes = [P for (P, flag) in zip(primes, good_flags) if flag]
aplist = [E.reduction(P).trace_of_frobenius() for P in good_primes[:30]]
f_aplist = [int(a) for a in f['hecke_eigenvalues'][:40]]
f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag][:30]
if aplist == f_aplist:
nok += 1
if verbose:
print("Curve %s and newform agree!" % ec['short_label'])
else:
print("Curve %s does NOT agree with newform" % ec['short_label'])
if verbose:
print("ap from curve: %s" % aplist)
print("ap from form: %s" % f_aplist)
if not ec['conductor_label'] in curve_ap:
curve_ap[ec['conductor_label']] = {}
form_ap[ec['conductor_label']] = {}
curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
else:
if verbose:
print("No curve with label %s found in the database!" % curve_label)
missing_curves.append(f['short_label'])
nnotfound += 1
# Report progress:
n = nfound + nnotfound
if nnotfound:
print("Out of %s newforms, %s curves were found in the database and %s were not found" % (n, nfound, nnotfound))
else:
print("Out of %s newforms, all %s had curves with the same label and ap" % (n, nfound))
if nfound == nok:
print("All curves agree with matching newforms")
else:
print("%s curves agree with matching newforms, %s do not" % (nok, nfound - nok))
if nnotfound:
print("%s missing curves" % len(missing_curves))
else:
return
# Step 2: for each newform for which there was no curve, call interface to Magma's EllipticCurveSearch()
if outfilename:
outfile = file(outfilename, mode="w")
def output(L):
if outfilename:
outfile.write(L)
if verbose:
sys.stdout.write(L)
for nf_label in missing_curves:
if verbose:
print("Curve %s is missing from the database..." % nf_label)
form = forms.find_one({'field_label': field_label, 'short_label': nf_label})
if not form:
print("... form %s not found!" % nf_label)
else:
if verbose:
print("... found form, calling Magma search")
N = K.ideal(form['level_label'])
neigs = len(form['hecke_eigenvalues'])
if verbose:
print("Using %s ap from Hilbert newform" % neigs)
Plist = [P['ideal'] for P in K.primes_iter(neigs)]
goodP = [(i, P) for i, P in enumerate(Plist) if not P.divides(N)]
aplist = [int(form['hecke_eigenvalues'][i]) for i, P in goodP]
curves = EllipticCurveSearch(K.K(), Plist, N, aplist)
if not curves:
if verbose:
print("No curves found by Magma, trying again...")
curves = EllipticCurveSearch(K.K(), Plist, N, aplist)
if verbose:
if curves:
print("Success!")
else:
print("Still no success, giving up")
#curves = EllipticCurveSearch(K.K(), [], N, [])
E = None
if curves:
E = curves[0]
print("%s curves for %s found, first is %s" % (len(curves),nf_label,E.ainvs()))
else:
print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!")
print("!!! No curves for %s found (using %s ap) !!!" % (nf_label,len(aplist)))
print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!")
if E!=None:
ec = {}
ec['field_label'] = field_label
ec['conductor_label'] = form['level_label']
ec['iso_label'] = form['label_suffix']
ec['number'] = int(1)
ec['conductor_ideal'] = form['level_ideal'].replace(" ","")
ec['conductor_norm'] = form['level_norm']
ai = E.ainvs()
ec['ainvs'] = [[str(c) for c in list(a)] for a in ai]
ec['cm'] = '?'
ec['base_change'] = []
output(make_curves_line(ec) + "\n")
if outfilename:
outfile.flush()
def check_curve_labels(field_label='2.2.5.1',
min_norm=0,
max_norm=None,
fix=False,
verbose=False):
r""" Go through all curves with the given field label, assumed totally
real, test whether a Hilbert Modular Form exists with the same
label.
"""
query = {}
query['field_label'] = field_label
query['number'] = 1 # only look at first curve in each isogeny class
query['conductor_norm'] = {'$gte': int(min_norm)}
if max_norm:
query['conductor_norm']['$lte'] = int(max_norm)
else:
max_norm = 'infinity'
cursor = nfcurves.find(query)
nfound = 0
nnotfound = 0
nok = 0
bad_curves = []
K = HilbertNumberField(field_label)
primes = [P['ideal'] for P in K.primes_iter(30)]
curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap
form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap
# Step 1: look at all curves (one per isogeny class), check that
# there is a Hilbert newform of the same label, and if so compare
# ap-lists. The dicts curve_ap and form_ap store these when
# there is disagreement:
# e.g. curve_ap[conductor_label][iso_label] = aplist.
for ec in cursor:
hmf_label = "-".join(
[ec['field_label'], ec['conductor_label'], ec['iso_label']])
f = forms.find_one({'field_label': field_label, 'label': hmf_label})
if f:
if verbose:
print("hmf with label %s found" % hmf_label)
nfound += 1
ainvsK = parse_ainvs(K.K(), ec['ainvs'])
E = EllipticCurve(ainvsK)
good_flags = [E.has_good_reduction(P) for P in primes]
good_primes = [P for (P, flag) in zip(primes, good_flags) if flag]
aplist = [
E.reduction(P).trace_of_frobenius() for P in good_primes[:10]
]
f_aplist = [int(a) for a in f['hecke_eigenvalues'][:30]]
f_aplist = [ap for ap, flag in zip(f_aplist, good_flags)
if flag][:10]
if aplist == f_aplist:
nok += 1
if verbose:
print("Curve %s and newform agree!" % ec['short_label'])
else:
bad_curves.append(ec['short_label'])
print("Curve %s does NOT agree with newform" %
ec['short_label'])
if verbose:
print("ap from curve: %s" % aplist)
print("ap from form: %s" % f_aplist)
if not ec['conductor_label'] in curve_ap:
curve_ap[ec['conductor_label']] = {}
form_ap[ec['conductor_label']] = {}
curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
else:
if verbose:
print("No hmf with label %s found!" % hmf_label)
nnotfound += 1
# Report progress:
n = nfound + nnotfound
if nnotfound:
print("Out of %s forms, %s were found and %s were not found" %
(n, nfound, nnotfound))
else:
print(
"Out of %s classes of curve, all %s had newforms with the same label"
% (n, nfound))
if nfound == nok:
print("All curves agree with matching newforms")
else:
print("%s curves agree with matching newforms, %s do not" %
(nok, nfound - nok))
# print("Bad curves: %s" % bad_curves)
# Step 2: for each conductor_label for which there was a
# discrepancy, create a dict giving the permutation curve -->
# newform, so remap[conductor_label][iso_label] = form_label
remap = {}
for level in curve_ap.keys():
remap[level] = {}
c_dat = curve_ap[level]
f_dat = form_ap[level]
for a in c_dat.keys():
aplist = c_dat[a]
for b in f_dat.keys():
if aplist == f_dat[b]:
remap[level][a] = b
break
if verbose:
print("remap: %s" % remap)
# Step 3, for through all curves with these bad conductors and
# create new labels for them, update the database with these (if
# fix==True)
for level in remap.keys():
perm = remap[level]
print("Fixing iso labels for conductor %s using map %s" %
(level, perm))
query = {}
query['field_label'] = field_label
query['conductor_label'] = level
cursor = nfcurves.find(query)
for ec in cursor:
iso = ec['iso_label']
if iso in perm:
new_iso = perm[iso]
if verbose:
print("--mapping class %s to class %s" % (iso, new_iso))
num = str(ec['number'])
newlabeldata = {}
newlabeldata['iso_label'] = new_iso
newlabeldata['short_class_label'] = '-'.join([level, new_iso])
newlabeldata['class_label'] = '-'.join(
[field_label, newlabeldata['short_class_label']])
newlabeldata['short_label'] = ''.join(
[newlabeldata['short_class_label'], num])
newlabeldata['label'] = '-'.join(
[field_label, newlabeldata['short_label']])
if verbose:
print("new data fields: %s" % newlabeldata)
if fix:
nfcurves.update({'_id': ec['_id']}, {"$set": newlabeldata},
upsert=True)
def find_curve_labels(field_label='2.2.5.1', min_norm=0, max_norm=None, outfilename=None, verbose=False):
r""" Go through all Hilbert Modular Forms with the given field label,
assumed totally real, for level norms in the given range, test
whether an elliptic curve exists with the same label.
"""
hmfs = conn.hmfs
forms = hmfs.forms
fields = hmfs.fields
query = {}
query['field_label'] = field_label
if fields.count({'label':field_label})==0:
if verbose:
print("No HMF data for field %s" % field_label)
return None
query['dimension'] = 1 # only look at rational newforms
query['level_norm'] = {'$gte' : int(min_norm)}
if max_norm:
query['level_norm']['$lte'] = int(max_norm)
else:
max_norm = 'infinity'
cursor = forms.find(query)
nfound = 0
nnotfound = 0
nok = 0
missing_curves = []
K = HilbertNumberField(field_label)
primes = [P['ideal'] for P in K.primes_iter(100)]
curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap
form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap
# Step 1: look at all newforms, check that there is an elliptic
# curve of the same label, and if so compare ap-lists. The
# dicts curve_ap and form_ap store these when there is
# disagreement: e.g. curve_ap[conductor_label][iso_label] =
# aplist.
for f in cursor:
curve_label = f['label']
ec = nfcurves.find_one({'field_label' : field_label, 'class_label' : curve_label, 'number' : 1})
if ec:
if verbose:
print("curve with label %s found" % curve_label)
nfound +=1
ainvsK = [K.K()([QQ(str(c)) for c in ai]) for ai in ec['ainvs']]
E = EllipticCurve(ainvsK)
good_flags = [E.has_good_reduction(P) for P in primes]
good_primes = [P for (P,flag) in zip(primes,good_flags) if flag]
aplist = [E.reduction(P).trace_of_frobenius() for P in good_primes[:30]]
f_aplist = [int(a) for a in f['hecke_eigenvalues'][:40]]
f_aplist = [ap for ap,flag in zip(f_aplist,good_flags) if flag][:30]
if aplist==f_aplist:
nok += 1
if verbose:
print("Curve %s and newform agree!" % ec['short_label'])
else:
print("Curve %s does NOT agree with newform" % ec['short_label'])
if verbose:
print("ap from curve: %s" % aplist)
print("ap from form: %s" % f_aplist)
if not ec['conductor_label'] in curve_ap:
curve_ap[ec['conductor_label']] = {}
form_ap[ec['conductor_label']] = {}
curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
else:
if verbose:
print("No curve with label %s found!" % curve_label)
missing_curves.append(f['short_label'])
nnotfound +=1
# Report progress:
n = nfound+nnotfound
if nnotfound:
print("Out of %s newforms, %s curves were found and %s were not found" % (n,nfound,nnotfound))
else:
print("Out of %s newforms, all %s had curves with the same label and ap" % (n,nfound))
if nfound==nok:
print("All curves agree with matching newforms")
else:
print("%s curves agree with matching newforms, %s do not" % (nok,nfound-nok))
if nnotfound:
print("Missing curves: %s" % missing_curves)
else:
return
# Step 2: for each newform for which there was no curve, create a
# Magma file containing code to search for such a curve.
# First output Magma code to define the field and primes:
if outfilename:
output_magma_field(field_label,K.K(),primes,outfilename)
if verbose:
print("...output definition of field and primes finished")
if outfilename:
outfile=file(outfilename, mode="a")
for nf_label in missing_curves:
if verbose:
print("Curve %s is missing..." % nf_label)
form = forms.find_one({'field_label':field_label, 'short_label':nf_label})
if not form:
print("... form %s not found!" % nf_label)
else:
if verbose:
print("... found form, outputting Magma search code")
output_magma_curve_search(K, form, outfilename, verbose=verbose)
def check_curve_labels(field_label='2.2.5.1', min_norm=0, max_norm=None, fix=False, verbose=False):
r""" Go through all curves with the given field label, assumed totally
real, test whether a Hilbert Modular Form exists with the same
label.
"""
hmfs = conn.hmfs
forms = hmfs.forms
fields = hmfs.fields
query = {}
query['field_label'] = field_label
query['number'] = 1 # only look at first curve in each isogeny class
query['conductor_norm'] = {'$gte' : int(min_norm)}
if max_norm:
query['conductor_norm']['$lte'] = int(max_norm)
else:
max_norm = 'infinity'
cursor = nfcurves.find(query)
nfound = 0
nnotfound = 0
nok = 0
bad_curves = []
K = HilbertNumberField(field_label)
primes = [P['ideal'] for P in K.primes_iter(30)]
curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap
form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap
# Step 1: look at all curves (one per isogeny class), check that
# there is a Hilbert newform of the same label, and if so compare
# ap-lists. The dicts curve_ap and form_ap store these when
# there is disagreement:
# e.g. curve_ap[conductor_label][iso_label] = aplist.
for ec in cursor:
hmf_label = "-".join([ec['field_label'],ec['conductor_label'],ec['iso_label']])
f = forms.find_one({'field_label' : field_label, 'label' : hmf_label})
if f:
if verbose:
print("hmf with label %s found" % hmf_label)
nfound +=1
ainvsK = [K.K()([QQ(str(c)) for c in ai]) for ai in ec['ainvs']]
E = EllipticCurve(ainvsK)
good_flags = [E.has_good_reduction(P) for P in primes]
good_primes = [P for (P,flag) in zip(primes,good_flags) if flag]
aplist = [E.reduction(P).trace_of_frobenius() for P in good_primes[:10]]
f_aplist = [int(a) for a in f['hecke_eigenvalues'][:30]]
f_aplist = [ap for ap,flag in zip(f_aplist,good_flags) if flag][:10]
if aplist==f_aplist:
nok += 1
if verbose:
print("Curve %s and newform agree!" % ec['short_label'])
else:
bad_curves.append(ec['short_label'])
print("Curve %s does NOT agree with newform" % ec['short_label'])
if verbose:
print("ap from curve: %s" % aplist)
print("ap from form: %s" % f_aplist)
if not ec['conductor_label'] in curve_ap:
curve_ap[ec['conductor_label']] = {}
form_ap[ec['conductor_label']] = {}
curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
else:
if verbose:
print("No hmf with label %s found!" % hmf_label)
nnotfound +=1
# Report progress:
n = nfound+nnotfound
if nnotfound:
print("Out of %s forms, %s were found and %s were not found" % (n,nfound,nnotfound))
else:
print("Out of %s classes of curve, all %s had newforms with the same label" % (n,nfound))
if nfound==nok:
print("All curves agree with matching newforms")
else:
print("%s curves agree with matching newforms, %s do not" % (nok,nfound-nok))
#print("Bad curves: %s" % bad_curves)
# Step 2: for each conductor_label for which there was a
# discrepancy, create a dict giving the permutation curve -->
# newform, so remap[conductor_label][iso_label] = form_label
remap = {}
for level in curve_ap.keys():
remap[level] = {}
c_dat = curve_ap[level]
f_dat = form_ap[level]
for a in c_dat.keys():
aplist = c_dat[a]
for b in f_dat.keys():
if aplist==f_dat[b]:
remap[level][a] = b
break
if verbose:
print("remap: %s" % remap)
# Step 3, for through all curves with these bad conductors and
# create new labels for them, update the database with these (if
# fix==True)
for level in remap.keys():
perm = remap[level]
print("Fixing iso labels for conductor %s using map %s" % (level,perm))
query = {}
query['field_label'] = field_label
query['conductor_label'] = level
cursor = nfcurves.find(query)
for ec in cursor:
iso = ec['iso_label']
if iso in perm:
new_iso = perm[iso]
if verbose:
print("--mapping class %s to class %s" % (iso,new_iso))
num = str(ec['number'])
newlabeldata = {}
newlabeldata['iso_label'] = new_iso
newlabeldata['short_class_label'] = '-'.join([level,new_iso])
newlabeldata['class_label'] = '-'.join([field_label,
newlabeldata['short_class_label']])
newlabeldata['short_label'] = ''.join([newlabeldata['short_class_label'],num])
newlabeldata['label'] = '-'.join([field_label,
newlabeldata['short_label']])
if verbose:
print("new data fields: %s" % newlabeldata)
if fix:
nfcurves.update({'_id': ec['_id']}, {"$set": newlabeldata}, upsert=True)
def find_curves(field_label='2.2.5.1', min_norm=0, max_norm=None, label=None, outfilename=None, verbose=False, effort=500):
r""" Go through all Hilbert Modular Forms with the given field label,
assumed totally real, for level norms in the given range, test
whether an elliptic curve exists with the same label; if not, find
the curves using Magma; output these to a file.
"""
print("Checking forms over {}, norms from {} to {}".format(field_label,min_norm,max_norm))
if outfilename:
print("Output of curves found to {}".format(outfilename))
else:
print("No curve search or output, just checking")
query = {}
query['field_label'] = field_label
if fields.find({'label': field_label}).count() == 0:
if verbose:
print("No HMF data for field %s" % field_label)
return None
query['dimension'] = 1 # only look at rational newforms
if label:
print("looking for {} only".format(label))
query['short_label'] = label # e.g. '91.1-a'
else:
query['level_norm'] = {'$gte': int(min_norm)}
if max_norm:
query['level_norm']['$lte'] = int(max_norm)
cursor = forms.find(query)
cursor.sort([('level_norm', pymongo.ASCENDING)])
labels = [f['label'] for f in cursor]
nfound = 0
nnotfound = 0
nok = 0
missing_curves = []
K = HilbertNumberField(field_label)
primes = [P['ideal'] for P in K.primes_iter(1000)]
curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap
form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap
# Step 1: look at all newforms, check that there is an elliptic
# curve of the same label, and if so compare ap-lists. The
# dicts curve_ap and form_ap store these when there is
# disagreement: e.g. curve_ap[conductor_label][iso_label] =
# aplist.
for curve_label in labels:
# We find the forms again since otherwise the cursor might timeout during the loop.
f = forms.find_one({'label': curve_label})
ec = nfcurves.find_one({'field_label': field_label, 'class_label': curve_label, 'number': 1})
if ec:
if verbose:
print("curve with label %s found in the database" % curve_label)
nfound += 1
ainvsK = parse_ainvs(K.K(), ec['ainvs'])
E = EllipticCurve(ainvsK)
good_flags = [E.has_good_reduction(P) for P in primes]
good_primes = [P for (P, flag) in zip(primes, good_flags) if flag]
aplist = [E.reduction(P).trace_of_frobenius() for P in good_primes]
f_aplist = [int(a) for a in f['hecke_eigenvalues']]
f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag]
nap = min(len(aplist), len(f_aplist))
if aplist[:nap] == f_aplist[:nap]:
nok += 1
if verbose:
print("Curve {} and newform agree! (checked {} ap)".format(ec['short_label'],nap))
else:
print("Curve {} does NOT agree with newform".format(ec['short_label']))
if verbose:
for P,aPf,aPc in zip(good_primes[:nap], f_aplist[:nap], aplist[:nap]):
if aPf!=aPc:
print("P = {} with norm {}".format(P,P.norm().factor()))
print("ap from curve: %s" % aPc)
print("ap from form: %s" % aPf)
if not ec['conductor_label'] in curve_ap:
curve_ap[ec['conductor_label']] = {}
form_ap[ec['conductor_label']] = {}
curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
else:
if verbose:
print("No curve with label %s found in the database!" % curve_label)
missing_curves.append(f['short_label'])
nnotfound += 1
# Report progress:
n = nfound + nnotfound
if nnotfound:
print("Out of %s newforms, %s curves were found in the database and %s were not found" % (n, nfound, nnotfound))
else:
print("Out of %s newforms, all %s had curves with the same label and ap" % (n, nfound))
if nfound == nok:
print("All curves agree with matching newforms")
else:
print("%s curves agree with matching newforms, %s do not" % (nok, nfound - nok))
if nnotfound:
print("%s missing curves" % len(missing_curves))
else:
return
# Step 2: for each newform for which there was no curve, call interface to Magma's EllipticCurveSearch()
# (unless outfilename is None in which case just dump the missing labels to a file)
if outfilename:
outfile = file(outfilename, mode="w")
else:
t = file("curves_missing.{}".format(field_label), mode="w")
for c in missing_curves:
t.write(c)
t.write("\n")
t.close()
return
def output(L):
if outfilename:
outfile.write(L)
if verbose:
sys.stdout.write(L)
bad_p = []
#if field_label=='4.4.1600.1': bad_p = [7**2,13**2,29**2]
if field_label=='4.4.2304.1': bad_p = [19**2,29**2]
if field_label=='4.4.4225.1': bad_p = [17**2,23**2]
if field_label=='4.4.7056.1': bad_p = [29**2,31**2]
if field_label=='4.4.7168.1': bad_p = [29**2]
if field_label=='4.4.9248.1': bad_p = [23**2]
if field_label=='4.4.11025.1': bad_p = [17**2,37**2,43**2]
if field_label=='4.4.13824.1': bad_p = [19**2]
if field_label=='4.4.12400.1': bad_p = [23**2]
if field_label=='4.4.180769.1': bad_p = [23**2]
if field_label=='6.6.905177.1': bad_p = [2**3]
bad_p = []
effort0 = effort
for nf_label in missing_curves:
if verbose:
print("Curve %s is missing from the database..." % nf_label)
form = forms.find_one({'field_label': field_label, 'short_label': nf_label})
if not form:
print("... form %s not found!" % nf_label)
else:
if verbose:
print("... found form, calling Magma search")
print("Conductor = %s" % form['level_ideal'].replace(" ",""))
N = K.ideal(form['level_label'])
neigs = len(form['hecke_eigenvalues'])
Plist = [P['ideal'] for P in K.primes_iter(neigs)]
goodP = [(i, P) for i, P in enumerate(Plist)
if not P.divides(N)
and not P.norm() in bad_p
and P.residue_class_degree()==1]
aplist = [int(form['hecke_eigenvalues'][i]) for i, P in goodP]
Plist = [P for i,P in goodP]
nap = len(Plist)
neigs0 = min(nap,100)
effort=effort0
if verbose:
print("Using %s ap from Hilbert newform and effort %s" % (neigs0,effort))
if bad_p:
print("( excluding primes with norms {})".format(bad_p))
#inds = list(set([randint(0,nap-1) for _ in range(neigs0)]))
inds = range(neigs0)
Plist0 = [Plist[i] for i in inds]
aplist0 = [aplist[i] for i in inds]
curves = EllipticCurveSearch(K.K(), Plist0, N, aplist0, effort)
# rep = 0
allrep=0
while not curves and allrep<10:
allrep += 1
effort*=2
# if rep<2:
# rep += 1
# else:
# rep = 1
# effort *=2
if verbose:
print("No curves found by Magma, trying again with effort %s..." % effort)
curves = EllipticCurveSearch(K.K(), Plist0, N, aplist0, effort)
if verbose:
if curves:
print("Success!")
else:
print("Still no success")
E = None
if curves:
E = curves[0]
print("%s curves for %s found, first is %s" % (len(curves),nf_label,E.ainvs()))
else:
print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!")
print("!!! No curves for %s found (using %s ap) !!!" % (nf_label,len(aplist)))
print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!")
if E!=None:
ec = {}
ec['field_label'] = field_label
ec['conductor_label'] = form['level_label']
ec['iso_label'] = form['label_suffix']
ec['number'] = int(1)
ec['conductor_ideal'] = form['level_ideal'].replace(" ","")
ec['conductor_norm'] = form['level_norm']
ai = E.ainvs()
ec['ainvs'] = ";".join([",".join([str(c) for c in list(a)]) for a in ai])
#print ec['ainvs']
ec['cm'] = '?'
ec['base_change'] = []
output(make_curves_line(ec) + "\n")
if outfilename:
outfile.flush()
def find_curve_labels(field_label='2.2.5.1',
min_norm=0,
max_norm=None,
outfilename=None,
verbose=False,
effort=1000):
r""" Go through all Hilbert Modular Forms with the given field label,
assumed totally real, for level norms in the given range, test
whether an elliptic curve exists with the same label.
"""
query = {}
query['field_label'] = field_label
if fields.find({'label': field_label}).count() == 0:
if verbose:
print("No HMF data for field %s" % field_label)
return None
query['dimension'] = 1 # only look at rational newforms
query['level_norm'] = {'$gte': int(min_norm)}
if max_norm:
query['level_norm']['$lte'] = int(max_norm)
else:
max_norm = 'infinity'
cursor = forms.find(query)
cursor.sort([('level_norm', pymongo.ASCENDING)])
labels = [f['label'] for f in cursor]
nfound = 0
nnotfound = 0
nok = 0
missing_curves = []
K = HilbertNumberField(field_label)
primes = [P['ideal'] for P in K.primes_iter()]
curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap
form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap
# Step 1: look at all newforms, check that there is an elliptic
# curve of the same label, and if so compare ap-lists. The
# dicts curve_ap and form_ap store these when there is
# disagreement: e.g. curve_ap[conductor_label][iso_label] =
# aplist.
for curve_label in labels:
# We find the forms again since otherwise the cursor might timeout during the loop.
f = forms.find_one({'label': curve_label})
ec = nfcurves.find_one({
'field_label': field_label,
'class_label': curve_label,
'number': 1
})
if ec:
if verbose:
print("curve with label %s found" % curve_label)
nfound += 1
ainvsK = parse_ainvs(K.K(), ec['ainvs'])
E = EllipticCurve(ainvsK)
good_flags = [E.has_good_reduction(P) for P in primes]
good_primes = [P for (P, flag) in zip(primes, good_flags) if flag]
aplist = [
E.reduction(P).trace_of_frobenius() for P in good_primes[:30]
]
f_aplist = [int(a) for a in f['hecke_eigenvalues'][:40]]
f_aplist = [ap for ap, flag in zip(f_aplist, good_flags)
if flag][:30]
if aplist == f_aplist:
nok += 1
if verbose:
print("Curve %s and newform agree!" % ec['short_label'])
else:
print("Curve %s does NOT agree with newform" %
ec['short_label'])
if verbose:
print("ap from curve: %s" % aplist)
print("ap from form: %s" % f_aplist)
if not ec['conductor_label'] in curve_ap:
curve_ap[ec['conductor_label']] = {}
form_ap[ec['conductor_label']] = {}
curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
else:
if verbose:
print("No curve with label %s found!" % curve_label)
missing_curves.append(f['short_label'])
nnotfound += 1
# Report progress:
n = nfound + nnotfound
if nnotfound:
print(
"Out of %s newforms, %s curves were found and %s were not found" %
(n, nfound, nnotfound))
else:
print(
"Out of %s newforms, all %s had curves with the same label and ap"
% (n, nfound))
if nfound == nok:
print("All curves agree with matching newforms")
else:
print("%s curves agree with matching newforms, %s do not" %
(nok, nfound - nok))
if nnotfound:
print("Missing curves: %s" % missing_curves)
else:
return
if outfilename == None:
return
# Step 2: for each newform for which there was no curve, create a
# Magma file containing code to search for such a curve.
# First output Magma code to define the field and primes:
output_magma_field(field_label, K.K(), primes, outfilename)
if verbose:
print("...output definition of field and primes finished")
for nf_label in missing_curves:
if verbose:
print("Curve %s is missing..." % nf_label)
form = forms.find_one({
'field_label': field_label,
'short_label': nf_label
})
if not form:
print("... form %s not found!" % nf_label)
else:
if verbose:
print("... found form, outputting Magma search code")
output_magma_curve_search(K,
form,
outfilename,
verbose=verbose,
effort=effort)
def find_curves(field_label='2.2.5.1',
min_norm=0,
max_norm=None,
label=None,
outfilename=None,
verbose=False,
effort=500):
r""" Go through all Hilbert Modular Forms with the given field label,
assumed totally real, for level norms in the given range, test
whether an elliptic curve exists with the same label; if not, find
the curves using Magma; output these to a file.
"""
print("Checking forms over {}, norms from {} to {}".format(
field_label, min_norm, max_norm))
if outfilename:
print("Output of curves found to {}".format(outfilename))
else:
print("No curve search or output, just checking")
query = {}
query['field_label'] = field_label
if fields.find({'label': field_label}).count() == 0:
if verbose:
print("No HMF data for field %s" % field_label)
return None
query['dimension'] = 1 # only look at rational newforms
if label:
print("looking for {} only".format(label))
query['short_label'] = label # e.g. '91.1-a'
else:
query['level_norm'] = {'$gte': int(min_norm)}
if max_norm:
query['level_norm']['$lte'] = int(max_norm)
cursor = forms.find(query)
cursor.sort([('level_norm', pymongo.ASCENDING)])
labels = [f['label'] for f in cursor]
nfound = 0
nnotfound = 0
nok = 0
missing_curves = []
K = HilbertNumberField(field_label)
primes = [P['ideal'] for P in K.primes_iter(1000)]
curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap
form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap
# Step 1: look at all newforms, check that there is an elliptic
# curve of the same label, and if so compare ap-lists. The
# dicts curve_ap and form_ap store these when there is
# disagreement: e.g. curve_ap[conductor_label][iso_label] =
# aplist.
for curve_label in labels:
# We find the forms again since otherwise the cursor might timeout during the loop.
f = forms.find_one({'label': curve_label})
ec = nfcurves.find_one({
'field_label': field_label,
'class_label': curve_label,
'number': 1
})
if ec:
if verbose:
print("curve with label %s found in the database" %
curve_label)
nfound += 1
ainvsK = parse_ainvs(K.K(), ec['ainvs'])
E = EllipticCurve(ainvsK)
good_flags = [E.has_good_reduction(P) for P in primes]
good_primes = [P for (P, flag) in zip(primes, good_flags) if flag]
aplist = [E.reduction(P).trace_of_frobenius() for P in good_primes]
f_aplist = [int(a) for a in f['hecke_eigenvalues']]
f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag]
nap = min(len(aplist), len(f_aplist))
if aplist[:nap] == f_aplist[:nap]:
nok += 1
if verbose:
print("Curve {} and newform agree! (checked {} ap)".format(
ec['short_label'], nap))
else:
print("Curve {} does NOT agree with newform".format(
ec['short_label']))
if verbose:
for P, aPf, aPc in zip(good_primes[:nap], f_aplist[:nap],
aplist[:nap]):
if aPf != aPc:
print("P = {} with norm {}".format(
P,
P.norm().factor()))
print("ap from curve: %s" % aPc)
print("ap from form: %s" % aPf)
if not ec['conductor_label'] in curve_ap:
curve_ap[ec['conductor_label']] = {}
form_ap[ec['conductor_label']] = {}
curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
else:
if verbose:
print("No curve with label %s found in the database!" %
curve_label)
missing_curves.append(f['short_label'])
nnotfound += 1
# Report progress:
n = nfound + nnotfound
if nnotfound:
print(
"Out of %s newforms, %s curves were found in the database and %s were not found"
% (n, nfound, nnotfound))
else:
print(
"Out of %s newforms, all %s had curves with the same label and ap"
% (n, nfound))
if nfound == nok:
print("All curves agree with matching newforms")
else:
print("%s curves agree with matching newforms, %s do not" %
(nok, nfound - nok))
if nnotfound:
print("%s missing curves" % len(missing_curves))
else:
return
# Step 2: for each newform for which there was no curve, call interface to Magma's EllipticCurveSearch()
# (unless outfilename is None in which case just dump the missing labels to a file)
if outfilename:
outfile = file(outfilename, mode="w")
else:
t = file("curves_missing.{}".format(field_label), mode="w")
for c in missing_curves:
t.write(c)
t.write("\n")
t.close()
return
def output(L):
if outfilename:
outfile.write(L)
if verbose:
sys.stdout.write(L)
bad_p = []
#if field_label=='4.4.1600.1': bad_p = [7**2,13**2,29**2]
if field_label == '4.4.2304.1': bad_p = [19**2, 29**2]
if field_label == '4.4.4225.1': bad_p = [17**2, 23**2]
if field_label == '4.4.7056.1': bad_p = [29**2, 31**2]
if field_label == '4.4.7168.1': bad_p = [29**2]
if field_label == '4.4.9248.1': bad_p = [23**2]
if field_label == '4.4.11025.1': bad_p = [17**2, 37**2, 43**2]
if field_label == '4.4.13824.1': bad_p = [19**2]
if field_label == '4.4.12400.1': bad_p = [23**2]
if field_label == '4.4.180769.1': bad_p = [23**2]
if field_label == '6.6.905177.1': bad_p = [2**3]
bad_p = []
effort0 = effort
for nf_label in missing_curves:
if verbose:
print("Curve %s is missing from the database..." % nf_label)
form = forms.find_one({
'field_label': field_label,
'short_label': nf_label
})
if not form:
print("... form %s not found!" % nf_label)
else:
if verbose:
print("... found form, calling Magma search")
print("Conductor = %s" % form['level_ideal'].replace(" ", ""))
N = K.ideal(form['level_label'])
neigs = len(form['hecke_eigenvalues'])
Plist = [P['ideal'] for P in K.primes_iter(neigs)]
goodP = [(i, P) for i, P in enumerate(Plist)
if not P.divides(N) and not P.norm() in bad_p
and P.residue_class_degree() == 1]
aplist = [int(form['hecke_eigenvalues'][i]) for i, P in goodP]
Plist = [P for i, P in goodP]
nap = len(Plist)
neigs0 = min(nap, 100)
effort = effort0
if verbose:
print("Using %s ap from Hilbert newform and effort %s" %
(neigs0, effort))
if bad_p:
print("( excluding primes with norms {})".format(bad_p))
#inds = list(set([randint(0,nap-1) for _ in range(neigs0)]))
inds = range(neigs0)
Plist0 = [Plist[i] for i in inds]
aplist0 = [aplist[i] for i in inds]
curves = EllipticCurveSearch(K.K(), Plist0, N, aplist0, effort)
# rep = 0
allrep = 0
while not curves and allrep < 10:
allrep += 1
effort *= 2
# if rep<2:
# rep += 1
# else:
# rep = 1
# effort *=2
if verbose:
print(
"No curves found by Magma, trying again with effort %s..."
% effort)
curves = EllipticCurveSearch(K.K(), Plist0, N, aplist0, effort)
if verbose:
if curves:
print("Success!")
else:
print("Still no success")
E = None
if curves:
E = curves[0]
print("%s curves for %s found, first is %s" %
(len(curves), nf_label, E.ainvs()))
else:
print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!")
print("!!! No curves for %s found (using %s ap) !!!" %
(nf_label, len(aplist)))
print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!")
if E != None:
ec = {}
ec['field_label'] = field_label
ec['conductor_label'] = form['level_label']
ec['iso_label'] = form['label_suffix']
ec['number'] = int(1)
ec['conductor_ideal'] = form['level_ideal'].replace(" ", "")
ec['conductor_norm'] = form['level_norm']
ai = E.ainvs()
ec['ainvs'] = ";".join(
[",".join([str(c) for c in list(a)]) for a in ai])
#print ec['ainvs']
ec['cm'] = '?'
ec['base_change'] = []
output(make_curves_line(ec) + "\n")
if outfilename:
outfile.flush()
