def set_info_for_web_newform(level=None, weight=None, character=None, label=None, **kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'bprec', default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm_cached(level=level, weight=weight, character=character, label=label)
emf_logger.critical("defined webnewform for rendering!")
# if info.has_key('download') and info.has_key('tempfile'):
# WNF._save_to_file(info['tempfile'])
# info['filename']=str(weight)+'-'+str(level)+'-'+str(character)+'-'+label+'.sobj'
# return info
except IndexError as e:
WNF = None
info['error'] = e.message
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
bread = [(EMF_TOP, url1)]
bread.append(("of level %s" % level, url2))
bread.append(("weight %s" % weight, url3))
if int(character) == 0:
bread.append(("trivial character", url4))
else:
bread.append(("\( %s \)" % (WNF.character.latex_name), url4))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',level=level, weight=weight, character=character)
friends.append(('\( S_{%s}(%s, %s)\)'%(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if hasattr(WNF.base_ring, "lmfdb_url") and WNF.base_ring.lmfdb_url:
friends.append(('Number field ' + WNF.base_ring.lmfdb_pretty, WNF.base_ring.lmfdb_url))
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_label:
friends.append(('Number field ' + WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_url))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)", WNF.character.url()))
if WNF.dimension==0:
info['error'] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
#info['name'] = name
info['title'] = 'Modular Form ' + WNF.hecke_orbit_label
if 'error' in info:
return info
# info['name']=WNF._name
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
## Example to illustrate the different cases
## base = CyclotomicField(n) -- of degree phi(n)
## coefficient_field = NumberField( p(x)) for some p in base['x'] of degree m
## we would then have cdeg = m*phi(n) and bdeg = phi(n)
## and rdeg = m
## Unfortunately, for e.g. base = coefficient_field = CyclotomicField(6)
## we get coefficient_field.relative_degree() == 2 although it should be 1
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if cdeg == 1:
rdeg = 1
else:
## just setting rdeg = WNF.coefficient_field.relative_degree() does not give correct result...
##
rdeg = QQ(cdeg)/QQ(bdeg)
cf_is_QQ = (cdeg == 1)
br_is_QQ = (bdeg == 1)
if cf_is_QQ:
info['satake'] = WNF.satake
info['qexp'] = WNF.q_expansion_latex(prec=10, name='\\alpha ')
info['qexp_display'] = url_for(".get_qexp_latex", level=level, weight=weight, character=character, label=label)
info['max_cn_qexp'] = WNF.q_expansion.prec()
## All combinations should be tested...
## 13/4/4/a -> base ring = coefficient_field = QQ(zeta_6)
## 13/3/8/a -> base_ring = QQ(zeta_4), coefficient_field has poly x^2+(2\zeta_4+2x-3\zeta_$ over base_ring
## 13/4/3/a -> base_ring = coefficient_field = QQ(zeta_3)
## 13/4/1/a -> all rational
## 13/6/1/a/ -> base_ring = QQ, coefficient_field = Q(sqrt(17))
## These are variables which needs to be set properly below
info['polvars'] = {'base_ring':'x','coefficient_field':'\\alpha'}
if not cf_is_QQ:
if rdeg>1: # not WNF.coefficient_field == WNF.base_ring:
## Here WNF.base_ring should be some cyclotomic field and we have an extension over this.
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1, '\\alpha') # make the variable \alpha
c_pol_ltx_x = web_latex_poly(p1, 'x')
zeta = p1.base_ring().gens()[0]
# p2 = zeta.minpoly() #this is not used anymore
# b_pol_ltx = web_latex_poly(p2, latex(zeta)) #this is not used anymore
z1 = zeta.multiplicative_order()
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'),c_pol_ltx_x, z1]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).</div><br/>'.format(c_pol_ltx)
info['polvars']['base_ring']='i'
elif z1<=2:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(c_pol_ltx)
else:
info['polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\) '%(c_pol_ltx, z1,z1)
info['polvars']['base_ring']='\zeta_{{ {0} }}'.format(z1)
if z1==3:
info['polynomial_st'] += 'is a primitive cube root of unity.'
else:
info['polynomial_st'] += 'is a primitive {0}-th root of unity.'.format(z1)
elif not br_is_QQ:
## Now we have base and coefficient field being equal, meaning that since the coefficient field is not QQ it is some cyclotomic field
## generated by some \zeta_n
p1 = WNF.coefficient_field.absolute_polynomial()
z1 = WNF.coefficient_field.gens()[0].multiplicative_order()
c_pol_ltx = web_latex_poly(p1, '\\zeta_{{{0}}}'.format(z1))
c_pol_ltx_x = web_latex_poly(p1, 'x')
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'), c_pol_ltx_x]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where \(\zeta_4=e^{{\\frac{{\\pi i}}{{ 2 }} }}=i \).</div>'.format(c_pol_ltx)
info['polvars']['coefficient_field']='i'
elif z1<=2:
info['polynomial_st'] = ''
else:
info['polynomial_st'] = '<div class="where">where \(\zeta_{{{0}}}=e^{{\\frac{{2\\pi i}}{{ {0} }} }}\) '.format(z1)
info['polvars']['coefficient_field']='\zeta_{{{0}}}'.format(z1)
if z1==3:
info['polynomial_st'] += 'is a primitive cube root of unity.</div>'
else:
info['polynomial_st'] += 'is a primitive {0}-th root of unity.</div>'.format(z1)
else:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg==1:
info['is_rational'] = 1
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty ]
else:
info['is_rational'] = 0
# info['q_exp_embeddings'] = WNF.print_q_expansion_embeddings()
# if(int(info['degree'])>1 and WNF.dimension()>1):
# s = 'One can embed it into \( \mathbb{C} \) as:'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# elif(int(info['degree'])>1):
# s = 'There are '+str(info['degree'])+' embeddings into \( \mathbb{C} \):'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# else:
# info['embeddings'] = ''
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings['values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = []
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'], list) and len(info['twist_info'])>0:
info['is_minimal'] = info['twist_info'][0]
if(info['twist_info'][0]):
s = 'Is minimal<br>'
else:
s = 'Is a twist of lower level<br>'
properties2 = [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 = [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm == 1:
info['cm_field'] = "2.0.{0}.1".format(-WNF.cm_disc)
info['cm_disc'] = WNF.cm_disc
info['cm_field_knowl'] = nf_display_knowl(info['cm_field'], getDBConnection(), field_pretty(info['cm_field']))
info['cm_field_url'] = url_for("number_fields.by_label", label=info["cm_field"])
if WNF.is_cm is None or WNF.is_cm==-1:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm == 1:
s = 'Is a CM-form<br>'
else:
s = 'Is not a CM-form<br>'
properties2.append(('CM info', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev,dict) and len(alev.keys())>0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if(level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6','')
if poly != '':
d,monom,coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(len(coeffs)):
c = QQ(coeffs[i])
s = ""
if d>1 and i >0 and c>0:
s="+"
if c<0:
s="-"
if c.denominator()>1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(abs(c.numerator()),c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]; b = monom[i][1]
if a == 0 and b != 0:
s+="E_6^{{ {0} }}".format(b)
elif b ==0 and a != 0:
s+="E_4^{{ {0} }}".format(a)
else:
s+="E_4^{{ {0} }}E_6^{{ {1} }}".format(a,b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if(label_other != label):
s = 'Modular form '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(label_other)
else:
s = s + str(level) + '.' + str(weight) + str(label_other)
url = url_for('emf.render_elliptic_modular_forms', level=level,
weight=weight, character=character, label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(label)
else:
s = s + str(level) + '.' + str(weight) + str(label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for(
'emf.render_elliptic_modular_forms', level=level, weight=weight, character=character, label=label)
if WNF.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_degree):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight == 2 and WNF.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_cn()
return info
def set_info_for_web_newform(level=None,
weight=None,
character=None,
label=None,
**kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(
level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'bprec', default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm_cached(level=level,
weight=weight,
character=character,
label=label,
prec=prec)
emf_logger.debug("defined webnewform for rendering!")
except IndexError as e:
WNF = None
info['error'] = e.message
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight,
character=character)
bread = [(EMF_TOP, url1)]
bread.append(("Level %s" % level, url2))
bread.append(("Weight %s" % weight, url3))
if int(character) == 0:
bread.append(("Trivial Character", url4))
else:
bread.append(("Character \( %s \)" % (WNF.character.latex_name), url4))
bread.append(
("Newform %d.%d.%d.%s" % (level, weight, int(character), label), ''))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character)
friends.append(
('\( S_{%s}(%s, %s)\)' %
(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if hasattr(WNF.base_ring, "lmfdb_url") and WNF.base_ring.lmfdb_url:
friends.append(('Number field ' + WNF.base_ring.lmfdb_pretty,
WNF.base_ring.lmfdb_url))
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_label:
friends.append(('Number field ' + WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_url))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)",
WNF.character.url()))
if WNF.dimension == 0:
info['error'] = "This space is empty!"
info['title'] = 'Newform ' + WNF.hecke_orbit_label
info['learnmore'] = [('History of Modular forms',
url_for('holomorphic_mf_history'))]
if 'error' in info:
return info
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
## Example to illustrate the different cases
## base = CyclotomicField(n) -- of degree phi(n)
## coefficient_field = NumberField( p(x)) for some p in base['x'] of degree m
## we would then have cdeg = m*phi(n) and bdeg = phi(n)
## and rdeg = m
## Unfortunately, for e.g. base = coefficient_field = CyclotomicField(6)
## we get coefficient_field.relative_degree() == 2 although it should be 1
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if cdeg == 1:
rdeg = 1
else:
## just setting rdeg = WNF.coefficient_field.relative_degree() does not give correct result...
##
rdeg = QQ(cdeg) / QQ(bdeg)
cf_is_QQ = (cdeg == 1)
br_is_QQ = (bdeg == 1)
if cf_is_QQ:
info['satake'] = WNF.satake
if WNF.complexity_of_first_nonvanishing_coefficients(
) > default_max_height:
info['qexp'] = ""
info['qexp_display'] = ''
info['hide_qexp'] = True
n, c = WNF.first_nonvanishing_coefficient()
info['trace_nv'] = latex(c.trace())
info['norm_nv'] = '\\approx ' + latex(c.norm().n())
info['index_nv'] = n
else:
info['qexp'] = WNF.q_expansion_latex(prec=10, name='\\alpha ')
info['qexp_display'] = url_for(".get_qexp_latex",
level=level,
weight=weight,
character=character,
label=label)
info["hide_qexp"] = False
info['max_cn_qexp'] = WNF.q_expansion.prec()
## All combinations should be tested...
## 13/4/4/a -> base ring = coefficient_field = QQ(zeta_6)
## 13/3/8/a -> base_ring = QQ(zeta_4), coefficient_field has poly x^2+(2\zeta_4+2x-3\zeta_$ over base_ring
## 13/4/3/a -> base_ring = coefficient_field = QQ(zeta_3)
## 13/4/1/a -> all rational
## 13/6/1/a/ -> base_ring = QQ, coefficient_field = Q(sqrt(17))
## These are variables which needs to be set properly below
info['polvars'] = {'base_ring': 'x', 'coefficient_field': '\\alpha'}
if not cf_is_QQ:
if rdeg > 1: # not WNF.coefficient_field == WNF.base_ring:
## Here WNF.base_ring should be some cyclotomic field and we have an extension over this.
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1,
'\\alpha') # make the variable \alpha
c_pol_ltx_x = web_latex_poly(p1, 'x')
zeta = p1.base_ring().gens()[0]
# p2 = zeta.minpoly() #this is not used anymore
# b_pol_ltx = web_latex_poly(p2, latex(zeta)) #this is not used anymore
z1 = zeta.multiplicative_order()
info['coeff_field'] = [
WNF.coefficient_field.absolute_polynomial_latex('x'),
c_pol_ltx_x, z1
]
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url,
WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_label
]
if z1 == 4:
info[
'polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).</div><br/>'.format(
c_pol_ltx)
info['polvars']['base_ring'] = 'i'
elif z1 <= 2:
info[
'polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(
c_pol_ltx)
else:
info[
'polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\) ' % (
c_pol_ltx, z1, z1)
info['polvars']['base_ring'] = '\zeta_{{ {0} }}'.format(z1)
if z1 == 3:
info[
'polynomial_st'] += 'is a primitive cube root of unity.'
else:
info[
'polynomial_st'] += 'is a primitive {0}-th root of unity.'.format(
z1)
elif not br_is_QQ:
## Now we have base and coefficient field being equal, meaning that since the coefficient field is not QQ it is some cyclotomic field
## generated by some \zeta_n
p1 = WNF.coefficient_field.absolute_polynomial()
z1 = WNF.coefficient_field.gens()[0].multiplicative_order()
c_pol_ltx = web_latex_poly(p1, '\\zeta_{{{0}}}'.format(z1))
c_pol_ltx_x = web_latex_poly(p1, 'x')
info['coeff_field'] = [
WNF.coefficient_field.absolute_polynomial_latex('x'),
c_pol_ltx_x
]
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url,
WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_label
]
if z1 == 4:
info[
'polynomial_st'] = '<div class="where">where \(\zeta_4=e^{{\\frac{{\\pi i}}{{ 2 }} }}=i \).</div>'.format(
c_pol_ltx)
info['polvars']['coefficient_field'] = 'i'
elif z1 <= 2:
info['polynomial_st'] = ''
else:
info[
'polynomial_st'] = '<div class="where">where \(\zeta_{{{0}}}=e^{{\\frac{{2\\pi i}}{{ {0} }} }}\) '.format(
z1)
info['polvars']['coefficient_field'] = '\zeta_{{{0}}}'.format(
z1)
if z1 == 3:
info[
'polynomial_st'] += 'is a primitive cube root of unity.</div>'
else:
info[
'polynomial_st'] += 'is a primitive {0}-th root of unity.</div>'.format(
z1)
else:
info['polynomial_st'] = ''
if info["hide_qexp"]:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg == 1:
info['is_rational'] = 1
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty
]
else:
info['is_rational'] = 0
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings[
'values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = [('Level', str(level)), ('Weight', str(weight)),
('Character', '$' + WNF.character.latex_name + '$'),
('Label', WNF.hecke_orbit_label),
('Dimension of Galois orbit', str(WNF.dimension))]
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'],
list) and len(info['twist_info']) > 0:
info['is_minimal'] = info['twist_info'][0]
if (info['twist_info'][0]):
s = 'Is minimal<br>'
else:
s = 'Is a twist of lower level<br>'
properties2 += [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 += [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm == 1:
info['cm_field'] = "2.0.{0}.1".format(-WNF.cm_disc)
info['cm_disc'] = WNF.cm_disc
info['cm_field_knowl'] = nf_display_knowl(
info['cm_field'], getDBConnection(),
field_pretty(info['cm_field']))
info['cm_field_url'] = url_for("number_fields.by_label",
label=info["cm_field"])
if WNF.is_cm is None or WNF.is_cm == -1:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm == 1:
s = 'Yes<br>'
else:
s = 'No<br>'
properties2.append(('CM', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev, dict) and len(alev.keys()) > 0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if (level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6', '')
if poly != '':
d, monom, coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(len(coeffs)):
c = QQ(coeffs[i])
s = ""
if d > 1 and i > 0 and c > 0:
s = "+"
if c < 0:
s = "-"
if c.denominator() > 1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(
abs(c.numerator()), c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]
b = monom[i][1]
if a == 0 and b != 0:
s += "E_6^{{ {0} }}".format(b)
elif b == 0 and a != 0:
s += "E_4^{{ {0} }}".format(a)
else:
s += "E_4^{{ {0} }}E_6^{{ {1} }}".format(a, b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if (label_other != label):
s = 'Modular form '
if character:
s += newform_label(level, weight, character, label_other)
else:
s += newform_label(level, weight, 1, label_other)
url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s += newform_label(level, weight, character, label)
else:
s += newform_label(level, weight, 1, label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label)
if WNF.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_degree):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight == 2 and WNF.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_available_prec()
return info
def make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [
c for c in db_ec().find({
'field_label': self.field_label,
'conductor_label': self.conductor_label,
'iso_label': self.iso_label
}).sort('number')
]
size = len(self.db_curves)
# Rank or bounds
try:
self.rk = web_latex(self.db_curves[0]['rank'])
except KeyError:
self.rk = "?"
try:
self.rk_bnds = "%s...%s" % tuple(self.db_curves[0]['rank_bounds'])
except KeyError:
self.rank_bounds = [0, sage.rings.infinity.Infinity]
self.rk_bnds = "not recorded"
# Extract the isogeny degree matrix from the database if possible, else create it
if hasattr(self, 'isogeny_matrix'):
from sage.matrix.all import Matrix
self.isogeny_matrix = Matrix(self.isogeny_matrix)
else:
self.isogeny_matrix = make_iso_matrix(self.db_curves)
# Create isogeny graph:
self.graph = make_graph(self.isogeny_matrix)
P = self.graph.plot(edge_labels=True)
self.graph_img = encode_plot(P)
self.graph_link = '<img src="%s" width="200" height="150"/>' % self.graph_img
self.isogeny_matrix_str = latex(matrix(self.isogeny_matrix))
self.field = field_pretty(self.field_label)
self.field_knowl = nf_display_knowl(self.field_label,
lmfdb.base.getDBConnection(),
self.field)
def curve_url(c):
return url_for(".show_ecnf",
nf=c['field_label'],
conductor_label=c['conductor_label'],
class_label=c['iso_label'],
number=c['number'])
self.curves = [[
c['short_label'],
curve_url(c),
web_ainvs(self.field_label, c['ainvs'])
] for c in self.db_curves]
self.urls = {}
self.urls['class'] = url_for(".show_ecnf_isoclass",
nf=self.field_label,
conductor_label=self.conductor_label,
class_label=self.iso_label)
self.urls['conductor'] = url_for(".show_ecnf_conductor",
nf=self.field_label,
conductor_label=self.conductor_label)
self.urls['field'] = url_for('.show_ecnf1', nf=self.field_label)
sig = self.signature
real_quadratic = sig == [2, 0]
totally_real = sig[1] == 0
imag_quadratic = sig == [0, 1]
if totally_real:
self.hmf_label = "-".join(
[self.field_label, self.conductor_label, self.iso_label])
self.urls['hmf'] = url_for('hmf.render_hmf_webpage',
field_label=self.field_label,
label=self.hmf_label)
self.urls['Lfunction'] = url_for("l_functions.l_function_hmf_page",
field=self.field_label,
label=self.hmf_label,
character='0',
number='0')
if imag_quadratic:
self.bmf_label = "-".join(
[self.field_label, self.conductor_label, self.iso_label])
self.friends = []
if totally_real:
self.friends += [('Hilbert Modular Form ' + self.hmf_label,
self.urls['hmf'])]
self.friends += [('L-function', self.urls['Lfunction'])]
if imag_quadratic:
self.friends += [
('Bianchi Modular Form %s not available' % self.bmf_label, '')
]
self.properties = [('Base field', self.field),
('Label', self.class_label),
(None, self.graph_link),
('Conductor', '%s' % self.conductor_label)]
if self.rk != '?':
self.properties += [('Rank', '%s' % self.rk)]
else:
if self.rk_bnds == 'not recorded':
self.properties += [('Rank', '%s' % self.rk_bnds)]
else:
self.properties += [('Rank bounds', '%s' % self.rk_bnds)]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.field_label, self.urls['field']),
(self.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.short_label,
self.urls['class'])]
def make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [c for c in db_ec().find(
{'field_label': self.field_label, 'conductor_label':
self.conductor_label, 'iso_label': self.iso_label}).sort('number')]
size = len(self.db_curves)
# Extract the isogeny degree matrix from the database if possible, else create it
if hasattr(self, 'isogeny_matrix'):
from sage.matrix.all import Matrix
self.isogeny_matrix = Matrix(self.isogeny_matrix)
else:
self.isogeny_matrix = make_iso_matrix(self.db_curves)
# Create isogeny graph:
self.graph = make_graph(self.isogeny_matrix)
P = self.graph.plot(edge_labels=True)
self.graph_img = encode_plot(P)
self.graph_link = '<img src="%s" width="200" height="150"/>' % self.graph_img
self.isogeny_matrix_str = latex(matrix(self.isogeny_matrix))
self.field = field_pretty(self.field_label)
self.field_knowl = nf_display_knowl(self.field_label, lmfdb.base.getDBConnection(), self.field)
def curve_url(c):
return url_for(".show_ecnf",
nf=c['field_label'],
conductor_label=c['conductor_label'],
class_label=c['iso_label'],
number=c['number'])
self.curves = [[c['short_label'], curve_url(c), web_ainvs(self.field_label,c['ainvs'])] for c in self.db_curves]
self.urls = {}
self.urls['class'] = url_for(".show_ecnf_isoclass", nf=self.field_label, conductor_label=self.conductor_label, class_label=self.iso_label)
self.urls['conductor'] = url_for(".show_ecnf_conductor", nf=self.field_label, conductor_label=self.conductor_label)
self.urls['field'] = url_for('.show_ecnf1', nf=self.field_label)
real_quadratic = self.signature == [2,0]
imag_quadratic = self.signature == [0,1]
if real_quadratic:
self.hmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.urls['hmf'] = url_for('hmf.render_hmf_webpage', field_label=self.field_label, label=self.hmf_label)
if imag_quadratic:
self.bmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.friends = []
if real_quadratic:
self.friends += [('Hilbert Modular Form ' + self.hmf_label, self.urls['hmf'])]
if imag_quadratic:
self.friends += [('Bianchi Modular Form %s not yet available' % self.bmf_label, '')]
self.properties = [('Base field', self.field),
('Label', self.class_label),
(None, self.graph_link),
('Conductor', '%s' % self.conductor_label)
]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.field_label, self.urls['field']),
(self.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.short_label, self.urls['class'])]
def set_info_for_web_newform(level=None, weight=None, character=None, label=None, **kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'bprec', default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm_cached(level=level, weight=weight, character=character, label=label)
emf_logger.critical("defined webnewform for rendering!")
# if info.has_key('download') and info.has_key('tempfile'):
# WNF._save_to_file(info['tempfile'])
# info['filename']=str(weight)+'-'+str(level)+'-'+str(character)+'-'+label+'.sobj'
# return info
except IndexError as e:
WNF = None
info['error'] = e.message
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
bread = [(EMF_TOP, url1)]
bread.append(("of level %s" % level, url2))
bread.append(("weight %s" % weight, url3))
if int(character) == 0:
bread.append(("trivial character", url4))
else:
bread.append(("\( %s \)" % (WNF.character.latex_name), url4))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',level=level, weight=weight, character=character)
friends.append(('\( S_{%s}(%s, %s)\)'%(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if hasattr(WNF.base_ring, "lmfdb_url") and WNF.base_ring.lmfdb_url:
friends.append(('Number field ' + WNF.base_ring.lmfdb_pretty, WNF.base_ring.lmfdb_url))
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_label:
friends.append(('Number field ' + WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_url))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)", WNF.character.url()))
if WNF.dimension==0:
info['error'] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
#info['name'] = name
info['title'] = 'Modular Form ' + WNF.hecke_orbit_label
if 'error' in info:
return info
# info['name']=WNF._name
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if cdeg == 1:
rdeg = 1
else:
rdeg = WNF.coefficient_field.relative_degree()
cf_is_QQ = (cdeg == 1)
br_is_QQ = (bdeg == 1)
if cf_is_QQ:
info['satake'] = WNF.satake
info['qexp'] = WNF.q_expansion_latex(prec=10, name='\\alpha ')
info['qexp_display'] = url_for(".get_qexp_latex", level=level, weight=weight, character=character, label=label)
info['max_cn_qexp'] = WNF.q_expansion.prec()
if not cf_is_QQ:
if not br_is_QQ and rdeg>1: # not WNF.coefficient_field == WNF.base_ring:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1, '\\alpha') # make the variable \alpha
c_pol_ltx_x = web_latex_poly(p1, 'x')
zeta = p1.base_ring().gens()[0]
# p2 = zeta.minpoly() #this is not used anymore
# b_pol_ltx = web_latex_poly(p2, latex(zeta)) #this is not used anymore
z1 = zeta.multiplicative_order()
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'),c_pol_ltx_x, z1]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).</div><br/>'.format(c_pol_ltx)
elif z1<=2:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(c_pol_ltx)
else:
info['polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\).'%(c_pol_ltx, z1,z1)
else:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1, '\\alpha')
c_pol_ltx_x = web_latex_poly(p1, 'x')
z1 = p1.base_ring().gens()[0].multiplicative_order()
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'), c_pol_ltx_x, z1]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).'.format(c_pol_ltx)
elif z1<=2:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(c_pol_ltx)
else:
info['polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\).'%(c_pol_ltx, z1,z1)
else:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg==1:
info['is_rational'] = 1
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty ]
else:
info['is_rational'] = 0
# info['q_exp_embeddings'] = WNF.print_q_expansion_embeddings()
# if(int(info['degree'])>1 and WNF.dimension()>1):
# s = 'One can embed it into \( \mathbb{C} \) as:'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# elif(int(info['degree'])>1):
# s = 'There are '+str(info['degree'])+' embeddings into \( \mathbb{C} \):'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# else:
# info['embeddings'] = ''
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings['values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = []
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'], list) and len(info['twist_info'])>0:
info['is_minimal'] = info['twist_info'][0]
if(info['twist_info'][0]):
s = 'Is minimal<br>'
else:
s = 'Is a twist of lower level<br>'
properties2 = [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 = [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm:
info['cm_field'] = "2.0.{0}.1".format(-WNF.cm_disc)
info['cm_disc'] = WNF.cm_disc
info['cm_field_knowl'] = nf_display_knowl(info['cm_field'], getDBConnection(), field_pretty(info['cm_field']))
info['cm_field_url'] = url_for("number_fields.by_label", label=info["cm_field"])
if WNF.is_cm is None:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm:
s = 'Is a CM-form<br>'
else:
s = 'Is not a CM-form<br>'
properties2.append(('CM info', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev,dict) and len(alev.keys())>0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if(level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6','')
if poly != '':
d,monom,coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(len(coeffs)):
c = QQ(coeffs[i])
s = ""
if d>1 and i >0 and c>0:
s="+"
if c<0:
s="-"
if c.denominator()>1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(abs(c.numerator()),c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]; b = monom[i][1]
if a == 0 and b != 0:
s+="E_6^{{ {0} }}".format(b)
elif b ==0 and a != 0:
s+="E_4^{{ {0} }}".format(a)
else:
s+="E_4^{{ {0} }}E_6^{{ {1} }}".format(a,b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if(label_other != label):
s = 'Modular form '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(label_other)
else:
s = s + str(level) + '.' + str(weight) + str(label_other)
url = url_for('emf.render_elliptic_modular_forms', level=level,
weight=weight, character=character, label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(label)
else:
s = s + str(level) + '.' + str(weight) + str(label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for(
'emf.render_elliptic_modular_forms', level=level, weight=weight, character=character, label=label)
if WNF.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_degree):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight == 2 and WNF.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_cn()
return info
def make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [c for c in db_ec().find(
{'field_label': self.field_label, 'conductor_label':
self.conductor_label, 'iso_label': self.iso_label}).sort('number')]
size = len(self.db_curves)
# Rank or bounds
try:
self.rk = web_latex(self.db_curves[0]['rank'])
except KeyError:
self.rk = "?"
try:
self.rk_bnds = "%s...%s" % tuple(self.db_curves[0]['rank_bounds'])
except KeyError:
self.rank_bounds = [0, sage.rings.infinity.Infinity]
self.rk_bnds = "not recorded"
# Extract the isogeny degree matrix from the database if possible, else create it
if hasattr(self, 'isogeny_matrix'):
from sage.matrix.all import Matrix
self.isogeny_matrix = Matrix(self.isogeny_matrix)
else:
self.isogeny_matrix = make_iso_matrix(self.db_curves)
# Create isogeny graph:
self.graph = make_graph(self.isogeny_matrix)
P = self.graph.plot(edge_labels=True)
self.graph_img = encode_plot(P)
self.graph_link = '<img src="%s" width="200" height="150"/>' % self.graph_img
self.isogeny_matrix_str = latex(matrix(self.isogeny_matrix))
self.field = field_pretty(self.field_label)
self.field_knowl = nf_display_knowl(self.field_label, lmfdb.base.getDBConnection(), self.field)
def curve_url(c):
return url_for(".show_ecnf",
nf=c['field_label'],
conductor_label=c['conductor_label'],
class_label=c['iso_label'],
number=c['number'])
self.curves = [[c['short_label'], curve_url(c), web_ainvs(self.field_label,c['ainvs'])] for c in self.db_curves]
self.urls = {}
self.urls['class'] = url_for(".show_ecnf_isoclass", nf=self.field_label, conductor_label=self.conductor_label, class_label=self.iso_label)
self.urls['conductor'] = url_for(".show_ecnf_conductor", nf=self.field_label, conductor_label=self.conductor_label)
self.urls['field'] = url_for('.show_ecnf1', nf=self.field_label)
sig = self.signature
real_quadratic = sig == [2,0]
totally_real = sig[1] == 0
imag_quadratic = sig == [0,1]
if totally_real:
self.hmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.urls['hmf'] = url_for('hmf.render_hmf_webpage', field_label=self.field_label, label=self.hmf_label)
self.urls['Lfunction'] = url_for("l_functions.l_function_hmf_page", field=self.field_label, label=self.hmf_label, character='0', number='0')
if imag_quadratic:
self.bmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.friends = []
if totally_real:
self.friends += [('Hilbert Modular Form ' + self.hmf_label, self.urls['hmf'])]
self.friends += [('L-function', self.urls['Lfunction'])]
if imag_quadratic:
self.friends += [('Bianchi Modular Form %s not available' % self.bmf_label, '')]
self.properties = [('Base field', self.field),
('Label', self.class_label),
(None, self.graph_link),
('Conductor', '%s' % self.conductor_label)
]
if self.rk != '?':
self.properties += [('Rank', '%s' % self.rk)]
else:
if self.rk_bnds == 'not recorded':
self.properties += [('Rank', '%s' % self.rk_bnds)]
else:
self.properties += [('Rank bounds', '%s' % self.rk_bnds)]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.field_label, self.urls['field']),
(self.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.short_label, self.urls['class'])]