def statistics_by_signature(d, r):
if d == 1:
return redirect(url_for("ec.statistics"))
info = {}
ecnfstats = db_ecnfstats()
sigs_by_deg = ecnfstats.find_one({'_id': 'signatures_by_degree'},
projection={'_id': False})
if not str(d) in sigs_by_deg:
info[
'error'] = "The database does not contain any elliptic curves defined over fields of degree %s" % d
else:
info['degree'] = d
if not r in range(d % 2, d + 1, 2):
info['error'] = "Invalid signature %s" % info['sig']
s = (d - r) // 2
info['sig'] = sig = '%s,%s' % (r, s)
info['summary'] = ecnf_signature_summary(sig)
fields_by_sig = ecnfstats.find_one({'_id': 'fields_by_signature'},
projection={'_id': False})
counts_by_field = ecnfstats.find_one({'_id': 'conductor_norm_by_field'},
projection={'_id': False})
def field_counts(f):
ff = f.replace(".", ":")
return [f, counts_by_field[ff]]
sorted_fields = sorted(fields_by_sig[sig], key=sort_field)
info['sig_stats'] = [field_counts(f) for f in sorted_fields]
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_signature(d, r):
if d == 1:
return redirect(url_for("ec.statistics"))
info = {}
ecnfstats = db.ec_nfcurves.stats
sigs_by_deg = ecnfstats.get_oldstat('signatures_by_degree')
if not str(d) in sigs_by_deg:
info[
'error'] = "The database does not contain any elliptic curves defined over fields of degree %s" % d
else:
info['degree'] = d
if not r in range(d % 2, d + 1, 2):
info['error'] = "Invalid signature %s" % info['sig']
s = (d - r) // 2
info['sig'] = sig = '%s,%s' % (r, s)
info['summary'] = ecnf_signature_summary(sig)
fields_by_sig = ecnfstats.get_oldstat('fields_by_signature')
counts_by_field = ecnfstats.get_oldstat('conductor_norm_by_field')
def field_counts(f):
ff = f.replace(".", ":")
return [f, counts_by_field[ff]]
sorted_fields = sorted(fields_by_sig[sig], key=sort_field)
info['sig_stats'] = [field_counts(f) for f in sorted_fields]
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_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_signature(d,r):
if d==1:
return redirect(url_for("ec.statistics"))
info = {}
ecnfstats = db_ecnfstats()
sigs_by_deg = ecnfstats.find_one({'_id':'signatures_by_degree'}, projection={'_id': False})
if not str(d) in sigs_by_deg:
info['error'] = "The database does not contain any elliptic curves defined over fields of degree %s" % d
else:
info['degree'] = d
if not r in range(d%2,d+1,2):
info['error'] = "Invalid signature %s" % info['sig']
s = (d-r)//2
info['sig'] = sig = '%s,%s' % (r,s)
info['summary'] = ecnf_signature_summary(sig)
fields_by_sig = ecnfstats.find_one({'_id':'fields_by_signature'}, projection={'_id': False})
counts_by_field = ecnfstats.find_one({'_id':'conductor_norm_by_field'}, projection={'_id': False})
def field_counts(f):
ff = f.replace(".",":")
return [f,counts_by_field[ff]]
sorted_fields = sorted(fields_by_sig[sig], key=sort_field)
info['sig_stats'] = [field_counts(f) for f in sorted_fields]
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_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()
)