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, 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'] = "[%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, 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'] = "[%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 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)]
label = form['short_label']
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()
