def allbsd(line):
r""" Parses one line from an allbsd file. Returns the label and a
dict containing fields with keys 'conductor', 'iso', 'number',
'ainvs', 'rank', 'torsion', 'torsion_primes', 'tamagawa_product',
'real_period', 'special_value', 'regulator', 'sha_an', 'sha',
'sha_primes', all values being strings or floats or ints or lists
of ints.
Input line fields:
conductor iso number ainvs rank torsion tamagawa_product real_period special_value regulator sha_an
Sample input line:
11 a 1 [0,-1,1,-10,-20] 0 5 5 1.2692093042795534217 0.25384186085591068434 1 1.00000000000000000000
"""
data = split(line)
label = data[0] + data[1] + data[2]
ainvs = parse_ainvs(data[3])
torsion = ZZ(data[5])
sha_an = RR(data[10])
sha = sha_an.round()
sha_primes = sha.prime_divisors()
torsion_primes = torsion.prime_divisors()
data = {
'conductor': int(data[0]),
'iso': data[0] + data[1],
'number': int(data[2]),
'ainvs': ainvs,
'rank': int(data[4]),
'tamagawa_product': int(data[6]),
'real_period': float(data[7]),
'special_value': float(data[8]),
'regulator': float(data[9]),
'sha_an': float(sha_an),
'sha': int(sha),
'sha_primes': [int(p) for p in sha_primes],
'torsion': int(torsion),
'torsion_primes': [int(p) for p in torsion_primes]
}
return label, data
def allbsd(line):
r""" Parses one line from an allbsd file. Returns the label and a
dict containing fields with keys 'conductor', 'iso', 'number',
'ainvs', 'rank', 'torsion', 'torsion_primes', 'tamagawa_product',
'real_period', 'special_value', 'regulator', 'sha_an', 'sha',
'sha_primes', all values being strings or floats or ints or lists
of ints.
Input line fields:
conductor iso number ainvs rank torsion tamagawa_product real_period special_value regulator sha_an
Sample input line:
11 a 1 [0,-1,1,-10,-20] 0 5 5 1.2692093042795534217 0.25384186085591068434 1 1.00000000000000000000
"""
data = split(line)
label = data[0] + data[1] + data[2]
ainvs = parse_ainvs(data[3])
torsion = ZZ(data[5])
sha_an = RR(data[10])
sha = sha_an.round()
sha_primes = sha.prime_divisors()
torsion_primes = torsion.prime_divisors()
data = {
'conductor': int(data[0]),
'iso': data[0] + data[1],
'number': int(data[2]),
'ainvs': ainvs,
'rank': int(data[4]),
'tamagawa_product': int(data[6]),
'real_period': float(data[7]),
'special_value': float(data[8]),
'regulator': float(data[9]),
'sha_an': float(sha_an),
'sha': int(sha),
'sha_primes': [int(p) for p in sha_primes],
'torsion': int(torsion),
'torsion_primes': [int(p) for p in torsion_primes]
}
return label, data
def add_sha_tor_primes(N1, N2):
"""
Add the 'sha', 'sha_primes', 'torsion_primes' fields to every
curve in the database whose conductor is between N1 and N2
inclusive.
"""
query = {}
query['conductor'] = {'$gte': int(N1), '$lte': int(N2)}
res = curves.find(query)
res = res.sort([('conductor', pymongo.ASCENDING)])
n = 0
for C in res:
label = C['lmfdb_label']
if n % 1000 == 0: print label
n += 1
torsion = ZZ(C['torsion'])
sha = RR(C['sha_an']).round()
sha_primes = sha.prime_divisors()
torsion_primes = torsion.prime_divisors()
data = {}
data['sha'] = int(sha)
data['sha_primes'] = [int(p) for p in sha_primes]
data['torsion_primes'] = [int(p) for p in torsion_primes]
curves.update({'lmfdb_label': label}, {"$set": data}, upsert=True)
def add_sha_tor_primes(N1,N2):
"""
Add the 'sha', 'sha_primes', 'torsion_primes' fields to every
curve in the database whose conductor is between N1 and N2
inclusive.
"""
query = {}
query['conductor'] = { '$gte': int(N1), '$lte': int(N2) }
res = curves.find(query)
res = res.sort([('conductor', pymongo.ASCENDING)])
n = 0
for C in res:
label = C['lmfdb_label']
if n%1000==0: print label
n += 1
torsion = ZZ(C['torsion'])
sha = RR(C['sha_an']).round()
sha_primes = sha.prime_divisors()
torsion_primes = torsion.prime_divisors()
data = {}
data['sha'] = int(sha)
data['sha_primes'] = [int(p) for p in sha_primes]
data['torsion_primes'] = [int(p) for p in torsion_primes]
curves.update({'lmfdb_label': label}, {"$set": data}, upsert=True)
def gl2_subgroup_data(label):
try:
data = db.gps_gl2zhat.lookup(label)
except ValueError:
return "Invalid label for subgroup of GL(2,Zhat): %s" % label
row_wrap = lambda cap, val: "<tr><td>%s: </td><td>%s</td></tr>\n" % (cap,
val)
matrix = lambda m: r'$\begin{bmatrix}%s&%s\\%s&%s\end{bmatrix}$' % (m[
0], m[1], m[2], m[3])
info = '<table>\n'
info += row_wrap(
'Subgroup <b>%s</b>' % (label),
"<small>" + ', '.join([matrix(m)
for m in data['generators']]) + "</small>")
info += "<tr><td></td><td></td></tr>\n"
info += row_wrap('Level', data['level'])
info += row_wrap('Index', data['index'])
info += row_wrap('Genus', data['genus'])
def ratcusps(c, r):
if not c:
return ""
if not r:
return " (none of which are rational)"
if r == c:
return " (all of which are rational)"
if r == 1:
return " (one of which is rational)"
else:
return " (of which %s are rational)" % r
info += row_wrap(
'Cusps', "%s%s" %
(data['cusps'], ratcusps(data['cusps'], data['rational_cusps'])))
info += row_wrap('Contains $-1$',
"yes" if data['quadratic_twists'][0] == label else "no")
if data.get('CPlabel'):
info += row_wrap(
'Cummins & Pauli label', "<a href=%scsg%sM.html#level%s>%s</a>" %
(CP_URL_PREFIX, data['genus'], data['level'], data['CPlabel']))
if data.get('RZBlabel'):
info += row_wrap(
'Rouse & Zureick-Brown label',
"<a href={prefix}{label}.html>{label}</a>".format(
prefix=RZB_URL_PREFIX, label=data['RZBlabel']))
if data.get('SZlabel'):
info += row_wrap('Sutherland & Zywina label', data['SZlabel'])
N = ZZ(data['level'])
ell = N.prime_divisors()[0]
e = N.valuation(ell)
if e == 1:
info += row_wrap(
"Cyclic %s-isogeny field degree" % (ell),
min([r[1] for r in data['isogeny_orbits'] if r[0] == ell]))
info += row_wrap("Cyclic %s-torsion field degree" % (ell),
min([r[1] for r in data['orbits'] if r[0] == ell]))
info += row_wrap(
"Full %s-torsion field degree" % (ell),
ell * (ell - 1) * (ell - 1) * (ell + 1) // data['index'])
else:
info += row_wrap(
"Cyclic %s${}^n$-isogeny field degrees" % (ell), ", ".join([
"%s" %
(min([r[1] for r in data['isogeny_orbits'] if r[0] == ell**n]))
for n in range(1, e + 1)
]))
info += row_wrap(
"Cyclic %s${}^n$-torsion field degrees" % (ell), ", ".join([
"%s" % (min([r[1] for r in data['orbits'] if r[0] == ell**n]))
for n in range(1, e + 1)
]))
info += row_wrap(
"Full %s${}^n$-torsion field degrees" % (ell), ", ".join([
"%s" % (ell * (ell - 1) * (ell - 1) *
(ell + 1) * ell**(4 * n) // data['index'])
for n in range(1, e + 1)
]))
if data['genus'] > 0:
info += row_wrap(
'Newforms', ''.join([
'<a href="%s">%s</a>' % (cmf_url_for_label(x), x)
for x in data['newforms']
]))
info += row_wrap('Analytic rank', data['rank'])
if data['genus'] == 1 and data['model']:
info += row_wrap(
'Model', '<a href="%s">%s</a>' % (url_for(
'ec.by_ec_label', label=data['model']), data['model']))
info += "</table>\n"
return info
