def browse():
info = {
'counts': get_stats().counts(),
'stats': get_stats().stats(),
}
credit = 'John Cremona'
t = 'Elliptic curves over number fields'
bread = [('Elliptic Curves', url_for("ecnf.index")),
('browse', ' ')]
return render_template("stats.html", info=info, credit=credit, title=t, bread=bread, learnmore=learnmore_list())
def browse():
info = {
'counts': get_stats().counts(),
'stats': get_stats().stats(),
}
credit = 'John Cremona'
t = 'Elliptic curves over number fields'
bread = [('Elliptic Curves', url_for("ecnf.index")),
('browse', ' ')]
return render_template("stats.html", info=info, credit=credit, title=t, bread=bread, learnmore=learnmore_list())
def statistics_by_signature(d, r):
info = {
'counts': get_stats().counts(),
'stats': get_stats().stats(),
'degree': d,
}
if isinstance(r, basestring):
info['sig_code'] = r
info['r'] = r = int(r[1:-1].split(",")[0])
else:
info['r'] = r
info['sig_code'] = '%s.%s' % (d, r),
info['sig'] = '(%s,%s)' % (r, (d - r) / 2)
info['sig_stats'] = ecnf_signature_summary(info['sig'])
if not d in info['counts']['degrees']:
if d == 1:
return redirect(url_for("ec.statistics"))
if d < 0:
info['error'] = "Negative degree!"
else:
info[
'error'] = "The database does not contain any elliptic curves defined over fields of degree %s" % d
if not r in range(d % 2, d + 1, 2):
info['error'] = "Invalid signature %s" % info['sig']
credit = 'John Cremona'
if info['sig'] == '(2,0)':
t = 'Elliptic curves over real quadratic number fields'
elif info['sig'] == '(0,1)':
t = 'Elliptic curves over imaginary quadratic number fields'
elif info['sig'] == '(3,0)':
t = 'Elliptic curves over totally real cubic number fields'
elif info['sig'] == '(1,1)':
t = 'Elliptic curves over mixed cubic number fields'
elif info['sig'] == '(4,0)':
t = 'Elliptic curves over totally real quartic number fields'
elif info['sig'] == '(5,0)':
t = 'Elliptic curves over totally real quintic number fields'
elif info['sig'] == '(6,0)':
t = 'Elliptic curves over totally real sextic number fields'
else:
t = 'Elliptic curves over number fields of degree %s, signature %s' % (
d, info['sig'])
bread = [('Elliptic Curves', url_for("ecnf.index")),
('degree %s' % d, url_for("ecnf.statistics_by_degree", d=d)),
('signature %s' % info['sig'], ' ')]
return render_template("ecnf-by-signature.html",
info=info,
credit=credit,
title=t,
bread=bread,
learnmore=learnmore_list())
def statistics_by_degree(d):
stats = get_stats()
info = {
'counts': stats.counts(),
'stats': stats.stats(),
'dstats': stats.dstats()[d],
'degree': d
}
if not d in info['counts']['degrees']:
if d==1:
return redirect(url_for("ec.statistics"))
if d<0:
info['error'] = "Negative degree!"
else:
info['error'] = "The database does not contain any elliptic curves defined over fields of degree %s" % d
info['degree_stats'] = ecnf_degree_summary(d)
sigs = ["(%s,%s)" % (r,(d-r)/2) for r in range(d%2,d+1,2)]
info['sig_stats'] = dict([(s,get_signature_stats(s)) for s in sigs])
credit = 'John Cremona'
if d==2:
t = 'Elliptic curves over quadratic number fields'
elif d==3:
t = 'Elliptic curves over cubic number fields'
elif d==4:
t = 'Elliptic curves over quartic number fields'
elif d==5:
t = 'Elliptic curves over quintic number fields'
elif d==6:
t = 'Elliptic curves over sextic number fields'
else:
t = 'Elliptic curves over number fields of degree %s' % d
bread = [('Elliptic Curves', url_for("ecnf.index")),
('degree %s' % d,' ')]
return render_template("by_degree.html", info=info, credit=credit, title=t, bread=bread, learnmore=learnmore_list())
def statistics_by_degree(d):
stats = get_stats()
info = {
'counts': stats.counts(),
'stats': stats.stats(),
'dstats': stats.dstats()[d],
'degree': d
}
if not d in info['counts']['degrees']:
if d==1:
return redirect(url_for("ec.statistics"))
if d<0:
info['error'] = "Negative degree!"
else:
info['error'] = "The database does not contain any elliptic curves defined over fields of degree %s" % d
info['degree_stats'] = ecnf_degree_summary(d)
sigs = ["(%s,%s)" % (r,(d-r)/2) for r in range(d%2,d+1,2)]
info['sig_stats'] = dict([(s,get_signature_stats(s)) for s in sigs])
credit = 'John Cremona'
if d==2:
t = 'Elliptic curves over quadratic number fields'
elif d==3:
t = 'Elliptic curves over cubic number fields'
elif d==4:
t = 'Elliptic curves over quartic number fields'
elif d==5:
t = 'Elliptic curves over quintic number fields'
elif d==6:
t = 'Elliptic curves over sextic number fields'
else:
t = 'Elliptic curves over number fields of degree %s' % d
bread = [('Elliptic Curves', url_for("ecnf.index")),
('degree %s' % d,' ')]
return render_template("by_degree.html", info=info, credit=credit, title=t, bread=bread, learnmore=learnmore_list())
def statistics_by_signature(d,r):
info = {
'counts': get_stats().counts(),
'stats': get_stats().stats(),
'degree': d,
}
if isinstance(r,basestring):
info['sig_code'] = r
info['r'] = r = int(r[1:-1].split(",")[0])
else:
info['r'] = r
info['sig_code'] = '%s.%s' % (d,r),
info['sig'] = '(%s,%s)' % (r,(d-r)/2)
info['sig_stats'] = ecnf_signature_summary(info['sig'])
if not d in info['counts']['degrees']:
if d==1:
return redirect(url_for("ec.statistics"))
if d<0:
info['error'] = "Negative degree!"
else:
info['error'] = "The database does not contain any elliptic curves defined over fields of degree %s" % d
if not r in range(d%2,d+1,2):
info['error'] = "Invalid signature %s" % info['sig']
credit = 'John Cremona'
if info['sig'] == '(2,0)':
t = 'Elliptic curves over real quadratic number fields'
elif info['sig'] == '(0,1)':
t = 'Elliptic curves over imaginary quadratic number fields'
elif info['sig'] == '(3,0)':
t = 'Elliptic curves over totally real cubic number fields'
elif info['sig'] == '(1,1)':
t = 'Elliptic curves over mixed cubic number fields'
elif info['sig'] == '(4,0)':
t = 'Elliptic curves over totally real quartic number fields'
elif info['sig'] == '(5,0)':
t = 'Elliptic curves over totally real quintic number fields'
elif info['sig'] == '(6,0)':
t = 'Elliptic curves over totally real sextic number fields'
else:
t = 'Elliptic curves over number fields of degree %s, signature %s' % (d,info['sig'])
bread = [('Elliptic Curves', url_for("ecnf.index")),
('degree %s' % d,url_for("ecnf.statistics_by_degree", d=d)),
('signature %s' % info['sig'],' ')]
return render_template("by_signature.html", info=info, credit=credit, title=t, bread=bread, learnmore=learnmore_list())
def statistics_by_signature(d, r):
info = {"counts": get_stats().counts(), "stats": get_stats().stats(), "degree": d}
if isinstance(r, basestring):
info["sig_code"] = r
info["r"] = r = int(r[1:-1].split(",")[0])
else:
info["r"] = r
info["sig_code"] = ("%s.%s" % (d, r),)
info["sig"] = "(%s,%s)" % (r, (d - r) / 2)
info["sig_stats"] = ecnf_signature_summary(info["sig"])
if not d in info["counts"]["degrees"]:
if d == 1:
return redirect(url_for("ec.statistics"))
if d < 0:
info["error"] = "Negative degree!"
else:
info["error"] = "The database does not contain any elliptic curves defined over fields of degree %s" % d
if not r in range(d % 2, d + 1, 2):
info["error"] = "Invalid signature %s" % info["sig"]
credit = "John Cremona"
if info["sig"] == "(2,0)":
t = "Elliptic curves over real quadratic number fields"
elif info["sig"] == "(0,1)":
t = "Elliptic curves over imaginary quadratic number fields"
elif info["sig"] == "(3,0)":
t = "Elliptic curves over totally real cubic number fields"
elif info["sig"] == "(1,1)":
t = "Elliptic curves over mixed cubic number fields"
elif info["sig"] == "(4,0)":
t = "Elliptic curves over totally real quartic number fields"
elif info["sig"] == "(5,0)":
t = "Elliptic curves over totally real quintic number fields"
elif info["sig"] == "(6,0)":
t = "Elliptic curves over totally real sextic number fields"
else:
t = "Elliptic curves over number fields of degree %s, signature %s" % (d, info["sig"])
bread = [
("Elliptic Curves", url_for("ecnf.index")),
("degree %s" % d, url_for("ecnf.statistics_by_degree", d=d)),
("signature %s" % info["sig"], " "),
]
return render_template(
"by_signature.html", info=info, credit=credit, title=t, 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(data=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:
counts = get_stats().counts()
data['fields'] = []
# Rationals
data['fields'].append(['the rational field', (('1.1.1.1', [url_for('ec.rational_elliptic_curves'), '$\Q$']),)])
# Real quadratics (only a sample)
rqfs = ['2.2.%s.1' % str(d) for d in [5, 89, 229, 497]]
nquadratics = counts['nfields_by_degree'][2]
niqfs = 5
nrqfs = nquadratics - niqfs
data['fields'].append(['%s real quadratic fields, including' % nrqfs, ((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)]) for nf in rqfs)])
# Imaginary quadratics
iqfs = ['2.0.%s.1' % str(d) for d in [4, 8, 3, 7, 11]]
data['fields'].append(['%s imaginary quadratic fields' % niqfs, ((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)]) for nf in iqfs)])
# Cubics
cubics = ['3.1.23.1'] + ['3.3.%s.1' % str(d) for d in [49,148,1957]]
ncubics = counts['nfields_by_degree'][3]
data['fields'].append(['%s cubic fields, including' % ncubics, ((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)]) for nf in cubics)])
# Quartics
quartics = ['4.4.%s.1' % str(d) for d in [725,2777,9909,19821]]
nquartics = counts['nfields_by_degree'][4]
data['fields'].append(['%s totally real quartic fields, including' % nquartics,
((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)]) for nf in quartics)])
# Quintics
quintics = ['5.5.%s.1' % str(d) for d in [14641]]
nquintics = counts['nfields_by_degree'][5]
data['fields'].append(['%s totally real quintic field' % nquintics, ((nf, [url_for('.show_ecnf1', nf=nf), field_pretty(nf)]) for nf in quintics)])
data['degrees'] = counts['degrees']
# 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_remove('Completeness'))
def index():
# if 'jump' in request.args:
# return show_ecnf1(request.args['label'])
if len(request.args) > 0:
return elliptic_curve_search(to_dict(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:
counts = get_stats().counts()
data['fields'] = []
# Rationals
data['fields'].append([
'the rational field',
(('1.1.1.1', [url_for('ec.rational_elliptic_curves'), '$\Q$']), )
])
# Real quadratics (only a sample)
rqfs = ['2.2.%s.1' % str(d) for d in [5, 89, 229, 497]]
nquadratics = counts['nfields_by_degree'].get(2, 0)
niqfs = 5
nrqfs = nquadratics - niqfs
data['fields'].append([
'%s real quadratic fields, including' % nrqfs,
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in rqfs)
])
# Imaginary quadratics
iqfs = ['2.0.%s.1' % str(d) for d in [4, 8, 3, 7, 11]]
data['fields'].append([
'%s imaginary quadratic fields' % niqfs,
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in iqfs)
])
# Cubics
cubics = ['3.1.23.1'] + ['3.3.%s.1' % str(d) for d in [49, 148, 1957]]
if 3 in counts['nfields_by_degree']:
ncubics = counts['nfields_by_degree'][3]
data['fields'].append([
'%s cubic fields, including' % ncubics,
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in cubics)
])
# Quartics
quartics = ['4.4.%s.1' % str(d) for d in [725, 2777, 9909, 19821]]
if 4 in counts['nfields_by_degree']:
nquartics = counts['nfields_by_degree'][4]
data['fields'].append([
'%s totally real quartic fields, including' % nquartics,
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in quartics)
])
# Quintics
quintics = [
'5.5.%s.1' % str(d) for d in [14641, 24217, 36497, 38569, 65657]
]
if 5 in counts['nfields_by_degree']:
nquintics = counts['nfields_by_degree'][5]
data['fields'].append([
'%s totally real quintic fields, including' % nquintics,
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in quintics)
])
# Sextics
sextics = [
'6.6.%s.1' % str(d) for d in [300125, 371293, 434581, 453789, 485125]
]
if 6 in counts['nfields_by_degree']:
nsextics = counts['nfields_by_degree'][6]
data['fields'].append([
'%s totally real sextic fields, including' % nsextics,
((nf, [url_for('.show_ecnf1', nf=nf),
field_pretty(nf)]) for nf in sextics)
])
data['degrees'] = sorted(counts['degrees'])
# 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_remove('Completeness'))
def browse():
info = {"counts": get_stats().counts(), "stats": get_stats().stats()}
credit = "John Cremona"
t = "Elliptic curves over number fields"
bread = [("Elliptic Curves", url_for("ecnf.index")), ("browse", " ")]
return render_template("stats.html", info=info, credit=credit, title=t, bread=bread, learnmore=learnmore_list())
def random_curve():
from sage.misc.prandom import randint
n = get_stats().counts()['ncurves']
n = randint(0,n-1)
E = db_ecnf().find()[n]
return redirect(url_for(".show_ecnf", nf=E['field_label'], conductor_label=E['conductor_label'], class_label=E['iso_label'], number=E['number']), 301)
