The default database of curves contains the following data:
Rank | Number of curves | Maximal conductor |
---|---|---|
0 | 30427 | 9999 |
1 | 31871 | 9999 |
2 | 2388 | 9999 |
3 | 836 | 119888 |
4 | 1 | 234446 |
5 | 1 | 19047851 |
6 | 1 | 5187563742 |
7 | 1 | 382623908456 |
8 | 1 | 457532830151317 |
AUTHOR: - William Stein (2007-10-07): initial version
See also the functions cremona_curves() and cremona_optimal_curves() which enable easy looping through the Cremona elliptic curve database.
Return a list of at most non-isogenous curves with given rank and torsion order.
INPUT:
OUTPUT:
(list) A list at most 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)