def rank(self, rank, tors=0, n=10, labels=False):
r"""
Return a list of at most `n` non-isogenous curves with given
rank and torsion order.
INPUT:
- ``rank`` (int) -- the desired rank
- ``tors`` (int, default 0) -- the desired torsion order (ignored if 0)
- ``n`` (int, default 10) -- the maximum number of curves returned.
- ``labels`` (bool, default False) -- if True, return Cremona
labels instead of curves.
OUTPUT:
(list) A list at most `n` of elliptic curves of required rank.
EXAMPLES::
sage: elliptic_curves.rank(n=5, rank=3, tors=2, labels=True)
['59450i1', '59450i2', '61376c1', '61376c2', '65481c1']
::
sage: elliptic_curves.rank(n=5, rank=0, tors=5, labels=True)
['11a1', '11a3', '38b1', '50b1', '50b2']
::
sage: elliptic_curves.rank(n=5, rank=1, tors=7, labels=True)
['574i1', '4730k1', '6378c1']
::
sage: e = elliptic_curves.rank(6)[0]; e.ainvs(), e.conductor()
((1, 1, 0, -2582, 48720), 5187563742)
sage: e = elliptic_curves.rank(7)[0]; e.ainvs(), e.conductor()
((0, 0, 0, -10012, 346900), 382623908456)
sage: e = elliptic_curves.rank(8)[0]; e.ainvs(), e.conductor()
((0, 0, 1, -23737, 960366), 457532830151317)
"""
from sage.misc.misc import SAGE_SHARE
db = os.path.join(SAGE_SHARE, 'ellcurves')
data = os.path.join(db, 'rank%s' % rank)
if not os.path.exists(data):
return []
v = []
tors = int(tors)
for w in open(data).readlines():
N, iso, num, ainvs, r, t = w.split()
if tors and tors != int(t):
continue
label = '%s%s%s' % (N, iso, num)
if labels:
v.append(label)
else:
E = EllipticCurve(eval(ainvs))
E._set_rank(r)
E._set_torsion_order(t)
E._set_conductor(N)
E._set_cremona_label(label)
v.append(E)
if len(v) >= n:
break
return v
def rank(self, rank, tors=0, n=10, labels=False):
r"""
Return a list of at most `n` non-isogenous curves with given
rank and torsion order.
INPUT:
- ``rank`` (int) -- the desired rank
- ``tors`` (int, default 0) -- the desired torsion order (ignored if 0)
- ``n`` (int, default 10) -- the maximum number of curves returned.
- ``labels`` (bool, default False) -- if True, return Cremona
labels instead of curves.
OUTPUT:
(list) A list at most `n` of elliptic curves of required rank.
EXAMPLES::
sage: elliptic_curves.rank(n=5, rank=3, tors=2, labels=True)
['59450i1', '59450i2', '61376c1', '61376c2', '65481c1']
::
sage: elliptic_curves.rank(n=5, rank=0, tors=5, labels=True)
['11a1', '11a3', '38b1', '50b1', '50b2']
::
sage: elliptic_curves.rank(n=5, rank=1, tors=7, labels=True)
['574i1', '4730k1', '6378c1']
::
sage: e = elliptic_curves.rank(6)[0]; e.ainvs(), e.conductor()
((1, 1, 0, -2582, 48720), 5187563742)
sage: e = elliptic_curves.rank(7)[0]; e.ainvs(), e.conductor()
((0, 0, 0, -10012, 346900), 382623908456)
sage: e = elliptic_curves.rank(8)[0]; e.ainvs(), e.conductor()
((0, 0, 1, -23737, 960366), 457532830151317)
"""
from sage.env import SAGE_SHARE
db = os.path.join(SAGE_SHARE, 'ellcurves')
data = os.path.join(db, 'rank%s' % rank)
if not os.path.exists(data):
return []
v = []
tors = int(tors)
for w in open(data).readlines():
N, iso, num, ainvs, r, t = w.split()
if tors and tors != int(t):
continue
label = '%s%s%s' % (N, iso, num)
if labels:
v.append(label)
else:
E = EllipticCurve(eval(ainvs))
E._set_rank(r)
E._set_torsion_order(t)
E._set_conductor(N)
E._set_cremona_label(label)
v.append(E)
if len(v) >= n:
break
return v
