def make_class(self):
curves_data = db_g2c().curves.find({
"class": self.label
}).sort([("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)])
self.curves = [{
"label": c['label'],
"equation_formatted": list_to_min_eqn(c['min_eqn']),
"url": url_for_label(c['label'])
} for c in curves_data]
self.ncurves = curves_data.count()
self.bad_lfactors = [[c[0],
list_to_factored_poly_otherorder(c[1])]
for c in self.bad_lfactors]
for endalgtype in [
'end_alg', 'rat_end_alg', 'real_end_alg', 'geom_end_alg',
'rat_geom_end_alg', 'real_geom_end_alg'
]:
if hasattr(self, endalgtype):
setattr(self, endalgtype + '_name',
end_alg_name(getattr(self, endalgtype)))
else:
setattr(self, endalgtype + '_name', '')
self.st_group_name = st_group_name(self.st_group)
if hasattr(self, 'geom_end_field') and self.geom_end_field <> '':
self.geom_end_field_name = field_pretty(self.geom_end_field)
else:
self.geom_end_field_name = ''
if self.is_gl2_type:
self.is_gl2_type_name = 'yes'
else:
self.is_gl2_type_name = 'no'
if hasattr(self, 'is_simple'):
if self.is_simple:
self.is_simple_name = 'yes'
else:
self.is_simple_name = 'no'
else:
self.is_simple_name = '?'
if hasattr(self, 'is_geom_simple'):
if self.is_geom_simple:
self.is_geom_simple_name = 'yes'
else:
self.is_geom_simple_name = 'no'
else:
self.is_geom_simple_name = '?'
x = self.label.split('.')[1]
self.friends = [('L-function',
url_for("l_functions.l_function_genus2_page",
cond=self.cond,
x=x)), ('Siegel modular form someday', '.')]
self.ecproduct_wurl = []
if hasattr(self, 'ecproduct'):
for i in range(2):
curve_label = self.ecproduct[i]
crv_url = url_for("ec.by_ec_label", label=curve_label)
if i == 1 or len(set(self.ecproduct)) <> 1:
self.friends.append(
('Elliptic curve ' + curve_label, crv_url))
self.ecproduct_wurl.append({
'label': curve_label,
'url': crv_url
})
self.ecquadratic_wurl = []
if hasattr(self, 'ecquadratic'):
for i in range(len(self.ecquadratic)):
curve_label = self.ecquadratic[i]
crv_spl = curve_label.split('-')
crv_url = url_for("ecnf.show_ecnf_isoclass",
nf=crv_spl[0],
conductor_label=crv_spl[1],
class_label=crv_spl[2])
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecquadratic_wurl.append({
'label': curve_label,
'url': crv_url,
'nf': crv_spl[0]
})
if hasattr(self, 'mfproduct'):
for i in range(len(self.mfproduct)):
mf_label = self.mfproduct[i]
mf_spl = mf_label.split('.')
mf_spl.append(mf_spl[2][-1])
mf_spl[2] = mf_spl[2][:-1] # Need a splitting function
mf_url = url_for("emf.render_elliptic_modular_forms",
level=mf_spl[0],
weight=mf_spl[1],
character=mf_spl[2],
label=mf_spl[3])
self.friends.append(('Modular form ' + mf_label, mf_url))
if hasattr(self, 'mfhilbert'):
for i in range(len(self.mfhilbert)):
mf_label = self.mfhilbert[i]
mf_spl = mf_label.split('-')
mf_url = url_for("hmf.render_hmf_webpage",
field_label=mf_spl[0],
label=mf_label)
self.friends.append(
('Hilbert modular form ' + mf_label, mf_url))
self.properties = [('Label', self.label),
('Number of curves', str(self.ncurves)),
('Conductor', '%s' % self.cond),
('Sato-Tate group', '\(%s\)' % self.st_group_name),
('\(\mathrm{End}(J_{\overline{\Q}}) \otimes \R\)',
'\(%s\)' % self.real_geom_end_alg_name),
('\(\mathrm{GL}_2\)-type',
'%s' % self.is_gl2_type_name)]
self.title = "Genus 2 Isogeny Class %s" % (self.label)
self.downloads = [
('Download Euler factors', ".")
] # url_for(".download_g2c_eulerfactors", label=self.label)),
# ('Download stored data for all curves', url_for(".download_g2c_all", label=self.label))]
self.bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % self.cond,
url_for(".by_conductor", conductor=self.cond)),
('%s' % self.label, ' ')]
def make_class(self):
curves_data = db_g2c().curves.find({"class" : self.label}).sort([("disc_key", pymongo.ASCENDING), ("label", pymongo.ASCENDING)])
self.curves = [ {"label" : c['label'], "equation_formatted" : list_to_min_eqn(c['min_eqn']), "url": url_for_label(c['label'])} for c in curves_data ]
self.ncurves = curves_data.count()
self.bad_lfactors = [ [c[0], list_to_factored_poly_otherorder(c[1])] for c in self.bad_lfactors]
for endalgtype in ['end_alg', 'rat_end_alg', 'real_end_alg', 'geom_end_alg', 'rat_geom_end_alg', 'real_geom_end_alg']:
if hasattr(self, endalgtype):
setattr(self,endalgtype + '_name',end_alg_name(getattr(self,endalgtype)))
else:
setattr(self,endalgtype + '_name','')
self.st_group_name = st_group_name(self.st_group)
if hasattr(self, 'geom_end_field') and self.geom_end_field <> '':
self.geom_end_field_name = field_pretty(self.geom_end_field)
else:
self.geom_end_field_name = ''
if self.is_gl2_type:
self.is_gl2_type_name = 'yes'
else:
self.is_gl2_type_name = 'no'
if hasattr(self, 'is_simple'):
if self.is_simple:
self.is_simple_name = 'yes'
else:
self.is_simple_name = 'no'
else:
self.is_simple_name = '?'
if hasattr(self, 'is_geom_simple'):
if self.is_geom_simple:
self.is_geom_simple_name = 'yes'
else:
self.is_geom_simple_name = 'no'
else:
self.is_geom_simple_name = '?'
x = self.label.split('.')[1]
self.friends = [
('L-function', url_for("l_functions.l_function_genus2_page", cond=self.cond,x=x)),
('Siegel modular form someday', '.')]
self.ecproduct_wurl = []
if hasattr(self, 'ecproduct'):
for i in range(2):
curve_label = self.ecproduct[i]
crv_url = url_for("ec.by_ec_label", label=curve_label)
if i == 1 or len(set(self.ecproduct)) <> 1:
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecproduct_wurl.append({'label' : curve_label, 'url' : crv_url})
self.ecquadratic_wurl = []
if hasattr(self, 'ecquadratic'):
for i in range(len(self.ecquadratic)):
curve_label = self.ecquadratic[i]
crv_spl = curve_label.split('-')
crv_url = url_for("ecnf.show_ecnf_isoclass", nf = crv_spl[0], conductor_label = crv_spl[1], class_label = crv_spl[2])
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecquadratic_wurl.append({'label' : curve_label, 'url' : crv_url, 'nf' : crv_spl[0]})
if hasattr(self, 'mfproduct'):
for i in range(len(self.mfproduct)):
mf_label = self.mfproduct[i]
mf_spl = mf_label.split('.')
mf_spl.append(mf_spl[2][-1])
mf_spl[2] = mf_spl[2][:-1] # Need a splitting function
mf_url = url_for("emf.render_elliptic_modular_forms", level=mf_spl[0], weight=mf_spl[1], character=mf_spl[2], label=mf_spl[3])
self.friends.append(('Modular form ' + mf_label, mf_url))
if hasattr(self, 'mfhilbert'):
for i in range(len(self.mfhilbert)):
mf_label = self.mfhilbert[i]
mf_spl = mf_label.split('-')
mf_url = url_for("hmf.render_hmf_webpage", field_label=mf_spl[0], label=mf_label)
self.friends.append(('Hilbert modular form ' + mf_label, mf_url))
self.properties = [('Label', self.label),
('Number of curves', str(self.ncurves)),
('Conductor','%s' % self.cond),
('Sato-Tate group', '\(%s\)' % self.st_group_name),
('\(\mathrm{End}(J_{\overline{\Q}}) \otimes \R\)','\(%s\)' % self.real_geom_end_alg_name),
('\(\mathrm{GL}_2\)-type','%s' % self.is_gl2_type_name)]
self.title = "Genus 2 Isogeny Class %s" % (self.label)
self.downloads = [
('Download Euler factors', ".")] # url_for(".download_g2c_eulerfactors", label=self.label)),
# ('Download stored data for all curves', url_for(".download_g2c_all", label=self.label))]
self.bread = [
('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % self.cond, url_for(".by_conductor", conductor=self.cond)),
('%s' % self.label, ' ')
]
g2c_columns = SearchColumns([
LinkCol("label", "g2c.label", "Label", url_for_curve_label, default=True),
ProcessedLinkCol("class", "g2c.isogeny_class", "Class", lambda v: url_for_isogeny_class_label(class_from_curve_label(v)), class_from_curve_label, default=True, orig="label"),
ProcessedCol("cond", "g2c.conductor", "Conductor", lambda v: web_latex(factor(v)), align="center", default=True),
MultiProcessedCol("disc", "ec.discriminant", "Discriminant", ["disc_sign", "abs_disc"], lambda s, a: web_latex_factored_integer(s*ZZ(a)),
default=lambda info: info.get("abs_disc"), align="center"),
MathCol("analytic_rank", "g2c.analytic_rank", "Rank*", default=True),
MathCol("two_selmer_rank", "g2c.two_selmer_rank", "2-Selmer rank"),
ProcessedCol("torsion_subgroup", "g2c.torsion", "Torsion",
lambda tors: r"\oplus".join([r"\Z/%s\Z"%n for n in literal_eval(tors)]) if tors != "[]" else r"\mathsf{trivial}",
default=True, mathmode=True, align="center"),
ProcessedCol("geom_end_alg", "g2c.geom_end_alg", r"$\textrm{End}^0(J_{\overline\Q})$", lambda v: r"\(%s\)"%geom_end_alg_name(v),
short_title="Qbar-end algebra", default=True, align="center"),
ProcessedCol("end_alg", "g2c.end_alg", r"$\textrm{End}^0(J)$", lambda v: r"\(%s\)"%end_alg_name(v), short_title="Q-end algebra", align="center"),
CheckCol("is_gl2_type", "g2c.gl2type", r"$\GL_2\textsf{-type}$", short_title="GL2-type"),
ProcessedCol("st_label", "g2c.st_group", "Sato-Tate", st_display_knowl, short_title='Sato-Tate group', align="center"),
CheckCol("is_simple_base", "ag.simple", r"$\Q$-simple", short_title="Q-simple"),
CheckCol("is_simple_geom", "ag.geom_simple", r"\(\overline{\Q}\)-simple", short_title="Qbar-simple"),
MathCol("aut_grp_tex", "g2c.aut_grp", r"\(\Aut(X)\)", short_title="Q-automorphisms"),
MathCol("geom_aut_grp_tex", "g2c.geom_aut_grp", r"\(\Aut(X_{\overline{\Q}})\)", short_title="Qbar-automorphisms"),
MathCol("num_rat_pts", "g2c.all_rational_points", r"$\Q$-points", short_title="Q-points*"),
MathCol("num_rat_wpts", "g2c.num_rat_wpts", r"$\Q$-Weierstrass points", short_title="Q-Weierstrass points"),
CheckCol("locally_solvable", "g2c.locally_solvable", "Locally solvable"),
CheckCol("has_square_sha", "g2c.analytic_sha", "Square ле*"),
MathCol("analytic_sha", "g2c.analytic_sha", "Analytic ле*"),
ProcessedCol("tamagawa_product", "g2c.tamagawa", "Tamagawa", lambda v: web_latex(factor(v)), short_title="Tamagawa product", align="center"),
ProcessedCol("regulator", "g2c.regulator", "Regulator", lambda v: r"\(%.6f\)"%v, align="right"),
ProcessedCol("real_period", "g2c.real_period", "Real period", lambda v: r"\(%.6f\)"%v, align="right"),
ProcessedCol("leading_coeff", "g2c.bsd_invariants", "Leading coefficient", lambda v: r"\(%.6f\)"%v, align="right"),
def make_class(self):
from lmfdb.genus2_curves.genus2_curve import url_for_curve_label
# Data
curves_data = g2cdb().curves.find({"class" : self.label},{'_id':int(0),'label':int(1),'min_eqn':int(1),'disc_key':int(1)}).sort([("disc_key", ASCENDING), ("label", ASCENDING)])
assert curves_data
self.curves = [ {"label" : c['label'], "equation_formatted" : list_to_min_eqn(c['min_eqn']),
"url": url_for_curve_label(c['label'])} for c in curves_data ]
self.ncurves = curves_data.count()
self.bad_lfactors = [ [c[0], list_to_factored_poly_otherorder(c[1])]
for c in self.bad_lfactors]
# Data derived from Sato-Tate group
self.st_group_name = st_group_name(self.st_group)
self.st_group_href = st_group_href(self.st_group)
self.st0_group_name = st0_group_name(self.real_geom_end_alg)
# Later used in Lady Gaga box:
self.real_geom_end_alg_disp = [r'\End(J_{\overline{\Q}}) \otimes \R',
end_alg_name(self.real_geom_end_alg)]
if self.is_gl2_type:
self.is_gl2_type_name = 'yes'
else:
self.is_gl2_type_name = 'no'
# Endomorphism data
endodata = g2cdb().endomorphisms.find_one({"label" :
self.curves[0]['label']})
self.gl2_statement_base = \
gl2_statement_base(endodata['factorsRR_base'], r'\(\Q\)')
self.endo_statement_base = \
"""Endomorphism algebra over \(\Q\):<br>""" + \
endo_statement_isog(endodata['factorsQQ_base'],
endodata['factorsRR_base'], r'')
endodata['fod_poly'] = intlist_to_poly(endodata['fod_coeffs'])
self.fod_statement = fod_statement(endodata['fod_label'],
endodata['fod_poly'])
if endodata['fod_label'] != '1.1.1.1':
self.endo_statement_geom = \
"""Endomorphism algebra over \(\overline{\Q}\):<br>""" + \
endo_statement_isog(endodata['factorsQQ_geom'],
endodata['factorsRR_geom'], r'\overline{\Q}')
else:
self.endo_statement_geom = ''
# Title
self.title = "Genus 2 Isogeny Class %s" % (self.label)
# Lady Gaga box
self.properties = (
('Label', self.label),
('Number of curves', str(self.ncurves)),
('Conductor','%s' % self.cond),
('Sato-Tate group', self.st_group_href),
('\(%s\)' % self.real_geom_end_alg_disp[0],
'\(%s\)' % self.real_geom_end_alg_disp[1]),
('\(\mathrm{GL}_2\)-type','%s' % self.is_gl2_type_name)
)
x = self.label.split('.')[1]
self.friends = [('L-function', url_for("l_functions.l_function_genus2_page", cond=self.cond,x=x))]
#self.downloads = [('Download Euler factors', ".")]
#self.downloads = [
# ('Download Euler factors', "."),
# url_for(".download_g2c_eulerfactors", label=self.label)),
# ('Download stored data for all curves',
# url_for(".download_g2c_all", label=self.label))
# ]
# Breadcrumbs
self.bread = (
('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % self.cond, url_for(".by_conductor", cond=self.cond)),
('%s' % self.label, ' ')
)
# More friends (NOTE: to be improved)
self.ecproduct_wurl = []
if hasattr(self, 'ecproduct'):
for i in range(2):
curve_label = self.ecproduct[i]
crv_url = url_for("ec.by_ec_label", label=curve_label)
if i == 1 or len(set(self.ecproduct)) != 1:
self.friends.append(('Elliptic curve ' + curve_label,
crv_url))
self.ecproduct_wurl.append({'label' : curve_label, 'url' :
crv_url})
self.ecquadratic_wurl = []
if hasattr(self, 'ecquadratic'):
for i in range(len(self.ecquadratic)):
curve_label = self.ecquadratic[i]
crv_spl = curve_label.split('-')
crv_url = url_for("ecnf.show_ecnf_isoclass", nf = crv_spl[0],
conductor_label = crv_spl[1], class_label = crv_spl[2])
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecquadratic_wurl.append({'label' : curve_label, 'url' :
crv_url, 'nf' : crv_spl[0]})
if hasattr(self, 'mfproduct'):
for i in range(len(self.mfproduct)):
mf_label = self.mfproduct[i]
mf_spl = mf_label.split('.')
mf_spl.append(mf_spl[2][-1])
mf_spl[2] = mf_spl[2][:-1] # Need a splitting function
mf_url = url_for("emf.render_elliptic_modular_forms",
level=mf_spl[0], weight=mf_spl[1], character=mf_spl[2],
label=mf_spl[3])
self.friends.append(('Modular form ' + mf_label, mf_url))
if hasattr(self, 'mfhilbert'):
for i in range(len(self.mfhilbert)):
mf_label = self.mfhilbert[i]
mf_spl = mf_label.split('-')
mf_url = url_for("hmf.render_hmf_webpage",
field_label=mf_spl[0], label=mf_label)
self.friends.append(('Hilbert modular form ' + mf_label, mf_url))
ProcessedCol("eqn",
"g2c.minimal_equation",
"Equation",
lambda v: min_eqn_pretty(literal_eval(v)),
default=True,
mathmode=True),
ProcessedCol("st_group",
"g2c.st_group",
"Sato-Tate",
lambda v: st_link_by_name(1, 4, v),
default=True,
align="center"),
ProcessedCol("end_alg",
"g2c.end_alg",
r"\(\Q\)-end algebra",
lambda v: r"\(%s\)" % end_alg_name(v),
short_title="Q-end algebra",
align="center"),
ProcessedCol("geom_end_alg",
"g2c.geom_end_alg",
r"\(\overline{\Q}\)-end algebra",
lambda v: r"\(%s\)" % geom_end_alg_name(v),
short_title="Qbar-end algebra",
align="center"),
CheckCol("is_simple_base",
"ag.simple",
r"\(\Q\)-simple",
short_title="Q-simple"),
CheckCol("is_simple_geom",
"ag.geom_simple",
r"\(\overline{\Q}\)-simple",