def make_extra_data(label, number, ainvs, gens):
"""Given a curve label (and number, as some data is only stored wih
curve number 1 in each class) and its ainvs and gens, returns a
dict with which to update the entry.
Extra items computed here:
'equation': latex string of curve's equation
'signD': sign of discriminant
'local_data': list of dicts, one item for each bad prime
'min_quad_twist': dict holding curve's min quadratic twist and the twisting discriminant
'heights': list of heights of gens
and for curve #1 in a class only:
'aplist': list of a_p for p<100
'anlist': list of a_n for n<=20
"""
E = EllipticCurve(parse_ainvs(ainvs))
data = {}
# convert from a list of strings to a single string, e.g. from ['0','0','0','1','1'] to '[0,0,0,1,1]'
data['equation'] = web_latex(E)
data['signD'] = int(E.discriminant().sign())
data['local_data'] = [{
'p':
int(ld.prime().gen()),
'ord_cond':
int(ld.conductor_valuation()),
'ord_disc':
int(ld.discriminant_valuation()),
'ord_den_j':
int(max(0, -(E.j_invariant().valuation(ld.prime().gen())))),
'red':
int(ld.bad_reduction_type()),
'rootno':
int(E.root_number(ld.prime().gen())),
'kod':
web_latex(ld.kodaira_symbol()).replace('$', ''),
'cp':
int(ld.tamagawa_number())
} for ld in E.local_data()]
Etw, Dtw = E.minimal_quadratic_twist()
if Etw.conductor() == E.conductor():
data['min_quad_twist'] = {'label': label, 'disc': int(1)}
else:
minq_ainvs = ''.join(['['] + [str(c) for c in Etw.ainvs()] + [']'])
r = curves.find_one({
'jinv': str(E.j_invariant()),
'ainvs': minq_ainvs
})
minq_label = "" if r is None else r['label']
data['min_quad_twist'] = {'label': minq_label, 'disc': int(Dtw)}
from lmfdb.elliptic_curves.web_ec import parse_points
gens = [E(g) for g in parse_points(gens)]
data['heights'] = [float(P.height()) for P in gens]
if number == 1:
data['aplist'] = E.aplist(100, python_ints=True)
data['anlist'] = E.anlist(20, python_ints=True)
return data
def make_extra_data(label, number, ainvs, gens):
"""
C is a database elliptic curve entry. Returns a dict with which to update the entry.
Data fields needed in C already: 'ainvs', 'lmfdb_label', 'gens', 'number'
"""
E = EllipticCurve([int(a) for a in ainvs])
data = {}
# convert from a list of strings to a single string, e.g. from ['0','0','0','1','1'] to '[0,0,0,1,1]'
data['xainvs'] = ''.join(['[', ','.join(ainvs), ']'])
data['equation'] = web_latex(E)
data['signD'] = int(E.discriminant().sign())
data['local_data'] = [{
'p':
int(ld.prime().gen()),
'ord_cond':
int(ld.conductor_valuation()),
'ord_disc':
int(ld.discriminant_valuation()),
'ord_den_j':
int(max(0, -(E.j_invariant().valuation(ld.prime().gen())))),
'red':
int(ld.bad_reduction_type()),
'rootno':
int(E.root_number(ld.prime().gen())),
'kod':
web_latex(ld.kodaira_symbol()).replace('$', ''),
'cp':
int(ld.tamagawa_number())
} for ld in E.local_data()]
Etw, Dtw = E.minimal_quadratic_twist()
if Etw.conductor() == E.conductor():
data['min_quad_twist'] = {'label': label, 'disc': int(1)}
else:
# Later this should be changed to look for xainvs but now all curves have ainvs
minq_ainvs = [str(c) for c in Etw.ainvs()]
r = curves.find_one({
'jinv': str(E.j_invariant()),
'ainvs': minq_ainvs
})
minq_label = "" if r is None else r['label']
data['min_quad_twist'] = {'label': minq_label, 'disc': int(Dtw)}
from lmfdb.elliptic_curves.web_ec import parse_points
gens = [E(g) for g in parse_points(gens)]
data['heights'] = [float(P.height()) for P in gens]
if number == 1:
data['aplist'] = E.aplist(100, python_ints=True)
data['anlist'] = E.anlist(20, python_ints=True)
return data
def make_extra_data(label,number,ainvs,gens):
"""Given a curve label (and number, as some data is only stored wih
curve number 1 in each class) and its ainvs and gens, returns a
dict with which to update the entry.
Extra items computed here:
'equation': latex string of curve's equation
'signD': sign of discriminant
'local_data': list of dicts, one item for each bad prime
'min_quad_twist': dict holding curve's min quadratic twist and the twisting discriminant
'heights': list of heights of gens
and for curve #1 in a class only:
'aplist': list of a_p for p<100
'anlist': list of a_n for n<=20
"""
E = EllipticCurve(parse_ainvs(ainvs))
data = {}
# convert from a list of strings to a single string, e.g. from ['0','0','0','1','1'] to '[0,0,0,1,1]'
data['equation'] = web_latex(E)
data['signD'] = int(E.discriminant().sign())
data['local_data'] = [{'p': int(ld.prime().gen()),
'ord_cond':int(ld.conductor_valuation()),
'ord_disc':int(ld.discriminant_valuation()),
'ord_den_j':int(max(0,-(E.j_invariant().valuation(ld.prime().gen())))),
'red':int(ld.bad_reduction_type()),
'rootno':int(E.root_number(ld.prime().gen())),
'kod':web_latex(ld.kodaira_symbol()).replace('$',''),
'cp':int(ld.tamagawa_number())}
for ld in E.local_data()]
Etw, Dtw = E.minimal_quadratic_twist()
if Etw.conductor()==E.conductor():
data['min_quad_twist'] = {'label':label, 'disc':int(1)}
else:
minq_ainvs = ''.join(['['] + [str(c) for c in Etw.ainvs()] + [']'])
r = curves.find_one({'jinv':str(E.j_invariant()), 'ainvs':minq_ainvs})
minq_label = "" if r is None else r['label']
data['min_quad_twist'] = {'label':minq_label, 'disc':int(Dtw)}
from lmfdb.elliptic_curves.web_ec import parse_points
gens = [E(g) for g in parse_points(gens)]
data['heights'] = [float(P.height()) for P in gens]
if number==1:
data['aplist'] = E.aplist(100,python_ints=True)
data['anlist'] = E.anlist(20,python_ints=True)
return data
def download_EC_all(label):
CDB = lmfdb.base.getDBConnection().elliptic_curves.curves
N, iso, number = split_lmfdb_label(label)
if number:
data = CDB.find_one({'lmfdb_label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
data_list = [data]
else:
data_list = sorted(list(CDB.find({'lmfdb_iso': label})),
key=lambda E: E['number'])
if len(data_list) == 0:
return elliptic_curve_jump_error(label, {})
# titles of all entries of curves
dump_data = []
titles = [str(c) for c in data_list[0]]
titles = [t for t in titles if t[0] != '_']
titles.sort()
dump_data.append(titles)
for data in data_list:
data1 = []
for t in titles:
d = data[t]
if t == 'ainvs':
data1.append(format_ainvs(d))
elif t in ['torsion_generators', 'torsion_structure']:
data1.append([eval(g) for g in d])
elif t == 'x-coordinates_of_integral_points':
data1.append(parse_list(d))
elif t == 'gens':
data1.append(parse_points(d))
elif t in ['iso', 'label', 'lmfdb_iso', 'lmfdb_label']:
data1.append(str(d))
else:
data1.append(d)
dump_data.append(data1)
response = make_response('\n'.join(str(an) for an in dump_data))
response.headers['Content-type'] = 'text/plain'
return response
def download_EC_all(label):
CDB = lmfdb.base.getDBConnection().elliptic_curves.curves
N, iso, number = split_lmfdb_label(label)
if number:
data = CDB.find_one({'lmfdb_label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
data_list = [data]
else:
data_list = sorted(list(CDB.find({'lmfdb_iso': label})), key=lambda E: E['number'])
if len(data_list) == 0:
return elliptic_curve_jump_error(label, {})
# titles of all entries of curves
dump_data = []
titles = [str(c) for c in data_list[0]]
titles = [t for t in titles if t[0] != '_']
titles.sort()
dump_data.append(titles)
for data in data_list:
data1 = []
for t in titles:
d = data[t]
if t == 'ainvs':
data1.append(format_ainvs(d))
elif t in ['torsion_generators', 'torsion_structure']:
data1.append([eval(g) for g in d])
elif t == 'x-coordinates_of_integral_points':
data1.append(parse_list(d))
elif t == 'gens':
data1.append(parse_points(d))
elif t in ['iso', 'label', 'lmfdb_iso', 'lmfdb_label']:
data1.append(str(d))
else:
data1.append(d)
dump_data.append(data1)
response = make_response('\n'.join(str(an) for an in dump_data))
response.headers['Content-type'] = 'text/plain'
return response
def download_EC_all(label):
CDB = lmfdb.base.getDBConnection().elliptic_curves.curves
N, iso, number = split_lmfdb_label(label)
if number:
data = CDB.find_one({"lmfdb_label": label})
if data is None:
return elliptic_curve_jump_error(label, {})
data_list = [data]
else:
data_list = sorted(list(CDB.find({"lmfdb_iso": label})), key=lambda E: E["number"])
if len(data_list) == 0:
return elliptic_curve_jump_error(label, {})
# titles of all entries of curves
dump_data = []
titles = [str(c) for c in data_list[0]]
titles = [t for t in titles if t[0] != "_"]
titles.sort()
dump_data.append(titles)
for data in data_list:
data1 = []
for t in titles:
d = data[t]
if t == "ainvs":
data1.append(format_ainvs(d))
elif t in ["torsion_generators", "torsion_structure"]:
data1.append([eval(g) for g in d])
elif t == "x-coordinates_of_integral_points":
data1.append(split_list(d))
elif t == "gens":
data1.append(parse_points(d))
elif t in ["iso", "label", "lmfdb_iso", "lmfdb_label"]:
data1.append(str(d))
else:
data1.append(d)
dump_data.append(data1)
response = make_response("\n".join(str(an) for an in dump_data))
response.headers["Content-type"] = "text/plain"
return response
def make_extra_data(label,number,ainvs,gens):
"""
C is a database elliptic curve entry. Returns a dict with which to update the entry.
Data fields needed in C already: 'ainvs', 'lmfdb_label', 'gens', 'number'
"""
E = EllipticCurve([int(a) for a in ainvs])
data = {}
# convert from a list of strings to a single string, e.g. from ['0','0','0','1','1'] to '[0,0,0,1,1]'
data['xainvs'] = ''.join(['[',','.join(ainvs),']'])
data['equation'] = web_latex(E)
data['signD'] = int(E.discriminant().sign())
data['local_data'] = [{'p': int(ld.prime().gen()),
'ord_cond':int(ld.conductor_valuation()),
'ord_disc':int(ld.discriminant_valuation()),
'ord_den_j':int(max(0,-(E.j_invariant().valuation(ld.prime().gen())))),
'red':int(ld.bad_reduction_type()),
'rootno':int(E.root_number(ld.prime().gen())),
'kod':web_latex(ld.kodaira_symbol()).replace('$',''),
'cp':int(ld.tamagawa_number())}
for ld in E.local_data()]
Etw, Dtw = E.minimal_quadratic_twist()
if Etw.conductor()==E.conductor():
data['min_quad_twist'] = {'label':label, 'disc':int(1)}
else:
# Later this should be changed to look for xainvs but now all curves have ainvs
minq_ainvs = [str(c) for c in Etw.ainvs()]
r = curves.find_one({'jinv':str(E.j_invariant()), 'ainvs':minq_ainvs})
minq_label = "" if r is None else r['label']
data['min_quad_twist'] = {'label':minq_label, 'disc':int(Dtw)}
from lmfdb.elliptic_curves.web_ec import parse_points
gens = [E(g) for g in parse_points(gens)]
data['heights'] = [float(P.height()) for P in gens]
if number==1:
data['aplist'] = E.aplist(100,python_ints=True)
data['anlist'] = E.anlist(20,python_ints=True)
return data
def allgens(line):
r""" Parses one line from an allgens file. Returns the label and
a dict containing fields with keys 'conductor', 'iso', 'number',
'ainvs', 'jinv', 'cm', 'rank', 'gens', 'torsion_order', 'torsion_structure',
'torsion_generators', all values being strings or ints, and more.
Input line fields:
conductor iso number ainvs rank torsion_structure gens torsion_gens
Sample input line:
20202 i 2 [1,0,0,-298389,54947169] 1 [2,4] [-570:6603:1] [-622:311:1] [834:19239:1]
"""
global lmfdb_label_to_label
global label_to_lmfdb_label
data = split(line)
iso = data[0] + data[1]
label = iso + data[2]
try:
lmfdb_label = label_to_lmfdb_label[label]
except AttributeError:
print("Label {} not found in label_to_lmfdb_label dict!".format(label))
lmfdb_label = ""
global nallgens
nallgens += 1
if nallgens % 100 == 0:
print("processing allgens for {} (#{})".format(label, nallgens))
rank = int(data[4])
t = data[5]
tor_struct = [] if t == '[]' else t[1:-1].split(",")
torsion = int(prod([int(ti) for ti in tor_struct], 1))
ainvs = parse_ainvs(data[3])
E = EllipticCurve(ainvs)
jinv = text_type(E.j_invariant())
if E.has_cm():
cm = int(E.cm_discriminant())
else:
cm = int(0)
N = E.conductor()
bad_p = N.prime_factors() # will be sorted
num_bad_p = len(bad_p)
local_data = [{
'p':
int(ld.prime().gen()),
'ord_cond':
int(ld.conductor_valuation()),
'ord_disc':
int(ld.discriminant_valuation()),
'ord_den_j':
int(max(0, -(E.j_invariant().valuation(ld.prime().gen())))),
'red':
int(ld.bad_reduction_type()),
'rootno':
int(E.root_number(ld.prime().gen())),
'kod':
web_latex(ld.kodaira_symbol()).replace('$', ''),
'cp':
int(ld.tamagawa_number())
} for ld in E.local_data()]
semistable = all([ld['ord_cond'] == 1 for ld in local_data])
gens = [
gen.replace("[", "(").replace("]", ")") for gen in data[6:6 + rank]
]
tor_gens = ["%s" % parse_tgens(tgens[1:-1]) for tgens in data[6 + rank:]]
from lmfdb.elliptic_curves.web_ec import parse_points
heights = [float(E(P).height()) for P in parse_points(gens)]
Etw, Dtw = E.minimal_quadratic_twist()
if Etw.conductor() == N:
min_quad_twist = {
'label': label,
'lmfdb_label': lmfdb_label,
'disc': int(1)
}
else:
minq_ainvs = Etw.ainvs()
r = curves.lucky({
'jinv': str(E.j_invariant()),
'ainvs': minq_ainvs
},
projection=['label', 'lmfdb_label'])
min_quad_twist = {
'label': r['label'],
'lmfdb_label': r['lmfdb_label'],
'disc': int(Dtw)
}
trace_hash = TraceHashClass(iso, E)
return label, {
'conductor': int(data[0]),
'iso': iso,
'number': int(data[2]),
'ainvs': ainvs,
'jinv': jinv,
'cm': cm,
'rank': rank,
'gens': gens,
'torsion': torsion,
'torsion_structure': tor_struct,
'torsion_generators': tor_gens,
'trace_hash': trace_hash,
'equation': web_latex(E),
'bad_primes': bad_p,
'num_bad_primes': num_bad_p,
'local_data': local_data,
'semistable': semistable,
'signD': int(E.discriminant().sign()),
'heights': heights,
'aplist': E.aplist(100, python_ints=True),
'anlist': E.anlist(20, python_ints=True),
'min_quad_twist': min_quad_twist,
}
