def browse():
data = ECNF_stats().sigs_by_deg
# We could use the dict directly but then could not control the order
# of the keys (degrees), so we use a list
info = [[d,['%s,%s'%sig for sig in data[d]]] for d in sorted(data.keys())]
credit = 'John Cremona'
t = 'Elliptic Curves over Number Fields'
bread = [('Elliptic Curves', url_for("ecnf.index")),
('Browse', ' ')]
return render_template("ecnf-stats.html", info=info, credit=credit, title=t, bread=bread, learnmore=learnmore_list())
def browse():
data = ECNF_stats().sigs_by_deg
# We could use the dict directly but then could not control the order
# of the keys (degrees), so we use a list
info = [[d, ['%s,%s' % sig for sig in data[d]]]
for d in sorted(data.keys())]
t = 'Elliptic curves over number fields'
bread = [('Elliptic curves', url_for("ecnf.index")), ('Browse', ' ')]
return render_template("ecnf-stats.html",
info=info,
title=t,
bread=bread,
learnmore=learnmore_list())
def index():
# if 'jump' in request.args:
# return show_ecnf1(request.args['label'])
info = to_dict(request.args, search_array=ECNFSearchArray())
if request.args:
return elliptic_curve_search(info)
bread = get_bread()
# the dict data will hold additional information to be displayed on
# the main browse and search page
# info['fields'] holds data for a sample of number fields of different
# signatures for a general browse:
fields_by_deg = ECNF_stats().fields_by_deg
fields_by_sig = ECNF_stats().fields_by_sig
info['fields'] = []
# Rationals
# info['fields'].append(['the rational field', (('1.1.1.1', [url_for('ec.rational_elliptic_curves'), '$\Q$']),)]) # Removed due to ambiguity
# Real quadratics (sample)
rqfs = ['2.2.{}.1'.format(d) for d in [5, 89, 229, 497]]
niqfs = len(fields_by_sig[0, 1])
nrqfs = len(fields_by_sig[2, 0])
info['fields'].append([
'{} real quadratic fields, including'.format(nrqfs),
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in rqfs)
])
# Imaginary quadratics (sample)
iqfs = ['2.0.{}.1'.format(d) for d in [4, 8, 3, 7, 11]]
info['fields'].append([
'{} imaginary quadratic fields, including'.format(niqfs),
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in iqfs)
])
# Cubics (sample)
cubics = ['3.1.23.1'] + ['3.3.{}.1'.format(d) for d in [49, 148, 1957]]
ncubics = len(fields_by_deg[3])
info['fields'].append([
'{} cubic fields, including'.format(ncubics),
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in cubics)
])
# Quartics (sample)
quartics = ['4.4.{}.1'.format(d) for d in [725, 2777, 9909, 19821]]
nquartics = len(fields_by_deg[4])
info['fields'].append([
'{} totally real quartic fields, including'.format(nquartics),
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in quartics)
])
# Quintics (sample)
quintics = [
'5.5.{}.1'.format(d) for d in [14641, 24217, 36497, 38569, 65657]
]
nquintics = len(fields_by_deg[5])
info['fields'].append([
'{} totally real quintic fields, including'.format(nquintics),
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in quintics)
])
# Sextics (sample)
sextics = [
'6.6.{}.1'.format(d) for d in [300125, 371293, 434581, 453789, 485125]
]
nsextics = len(fields_by_deg[6])
info['fields'].append([
'{} totally real sextic fields, including'.format(nsextics),
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in sextics)
])
info['degrees'] = sorted(
[int(d) for d in fields_by_deg.keys() if d != '_id'])
# info['highlights'] holds data (URL and descriptive text) for a
# sample of elliptic curves with interesting features:
info['highlights'] = []
info['highlights'].append([
'A curve with $C_3\\times C_3$ torsion',
url_for('.show_ecnf',
nf='2.0.3.1',
class_label='a',
conductor_label='2268.36.18',
number=int(1))
])
info['highlights'].append([
'A curve with $C_4\\times C_4$ torsion',
url_for('.show_ecnf',
nf='2.0.4.1',
class_label='b',
conductor_label='5525.870.5',
number=int(9))
])
info['highlights'].append([
'A curve with CM by $\\sqrt{-267}$',
url_for('.show_ecnf',
nf='2.2.89.1',
class_label='a',
conductor_label='81.1',
number=int(1))
])
info['highlights'].append([
'An isogeny class with isogenies of degree $3$ and $89$ (and $267$)',
url_for('.show_ecnf_isoclass',
nf='2.2.89.1',
class_label='a',
conductor_label='81.1')
])
info['highlights'].append([
'A curve with everywhere good reduction, but no global minimal model',
url_for('.show_ecnf',
nf='2.2.229.1',
class_label='a',
conductor_label='1.1',
number=int(1))
])
return render_template("ecnf-index.html",
title="Elliptic Curves over Number Fields",
info=info,
bread=bread,
learnmore=learnmore_list())
def index():
# if 'jump' in request.args:
# return show_ecnf1(request.args['label'])
if len(request.args) > 0:
return elliptic_curve_search(request.args)
bread = get_bread()
# the dict data will hold additional information to be displayed on
# the main browse and search page
data = {}
# data['fields'] holds data for a sample of number fields of different
# signatures for a general browse:
fields_by_deg = ECNF_stats().fields_by_deg
fields_by_sig = ECNF_stats().fields_by_sig
data['fields'] = []
# Rationals
data['fields'].append(['the rational field', (('1.1.1.1', [url_for('ec.rational_elliptic_curves'), '$\Q$']),)])
# Real quadratics (sample)
rqfs = ['2.2.{}.1'.format(d) for d in [5, 89, 229, 497]]
niqfs = len(fields_by_sig[0,1])
nrqfs = len(fields_by_sig[2,0])
data['fields'].append(['{} real quadratic fields, including'.format(nrqfs),
((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)])
for nf in rqfs)])
# Imaginary quadratics (sample)
iqfs = ['2.0.{}.1'.format(d) for d in [4, 8, 3, 7, 11]]
data['fields'].append(['{} imaginary quadratic fields, including'.format(niqfs),
((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)])
for nf in iqfs)])
# Cubics (sample)
cubics = ['3.1.23.1'] + ['3.3.{}.1'.format(d) for d in [49,148,1957]]
ncubics = len(fields_by_deg[3])
data['fields'].append(['{} cubic fields, including'.format(ncubics),
((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)])
for nf in cubics)])
# Quartics (sample)
quartics = ['4.4.{}.1'.format(d) for d in [725,2777,9909,19821]]
nquartics = len(fields_by_deg[4])
data['fields'].append(['{} totally real quartic fields, including'.format(nquartics),
((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)])
for nf in quartics)])
# Quintics (sample)
quintics = ['5.5.{}.1'.format(d) for d in [14641, 24217, 36497, 38569, 65657]]
nquintics = len(fields_by_deg[5])
data['fields'].append(['{} totally real quintic fields, including'.format(nquintics),
((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)])
for nf in quintics)])
# Sextics (sample)
sextics = ['6.6.{}.1'.format(d) for d in [300125, 371293, 434581, 453789, 485125]]
nsextics = len(fields_by_deg[6])
data['fields'].append(['{} totally real sextic fields, including'.format(nsextics),
((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)])
for nf in sextics)])
data['degrees'] = sorted([int(d) for d in fields_by_deg.keys() if d!='_id'])
# data['highlights'] holds data (URL and descriptive text) for a
# sample of elliptic curves with interesting features:
data['highlights'] = []
data['highlights'].append(
['A curve with $C_3\\times C_3$ torsion',
url_for('.show_ecnf', nf='2.0.3.1', class_label='a', conductor_label='2268.36.18', number=int(1))]
)
data['highlights'].append(
['A curve with $C_4\\times C_4$ torsion',
url_for('.show_ecnf', nf='2.0.4.1', class_label='b', conductor_label='5525.870.5', number=int(9))]
)
data['highlights'].append(
['A curve with CM by $\\sqrt{-267}$',
url_for('.show_ecnf', nf='2.2.89.1', class_label='a', conductor_label='81.1', number=int(1))]
)
data['highlights'].append(
['An isogeny class with isogenies of degree $3$ and $89$ (and $267$)',
url_for('.show_ecnf_isoclass', nf='2.2.89.1', class_label='a', conductor_label='81.1')]
)
data['highlights'].append(
['A curve with everywhere good reduction, but no global minimal model',
url_for('.show_ecnf', nf='2.2.229.1', class_label='a', conductor_label='1.1', number=int(1))]
)
return render_template("ecnf-index.html",
title="Elliptic Curves over Number Fields",
data=data,
bread=bread, learnmore=learnmore_list())