A110620 Number of elliptic curves (up to isomorphism) of conductor n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 6, 8, 0, 4, 0, 3, 4, 6, 0, 0, 6, 0, 5, 4, 0, 0, 8, 0, 4, 4, 4, 3, 4, 4, 5, 4, 4, 0, 6, 1, 2, 8, 2, 0, 6, 4, 8, 2, 2, 1, 6, 4, 6, 7, 3, 0, 0, 1, 4, 6, 4, 2, 12, 1, 0, 2, 4, 0, 6, 2, 0, 12, 1, 6, 4, 1, 8, 0, 2, 1, 6, 2, 0, 0, 1, 3, 16, 4, 3, 0, 2, 0, 8, 0, 6, 11, 4, 1, 12, 0

Offset

1,11

Links

J. E. Cremona, Table of n, a(n) for n = 1..10000

A. Brumer and J. H. Silverman, The number of elliptic curves over Q with conductor N, Manuscripta Math. 91 (1996), no. 1, 95-102.

J. E. Cremona, Elliptic Curve Data.

LMFDB, Elliptic curves over Q.

Example

a(11)=3 since there are three non-isomorphic elliptic curves of conductor eleven, represented by the minimal models y^2+y=x^3-x^2-10*x-20, y^2+y=x^3-x^2-7820*x-263580 and y^2+y=x^3-x^2.

Prog

(Sage)  # Uses Cremona's database of elliptic curves (works for all n < 500000)
def a(n):
    return CremonaDatabase().number_of_curves(n)  # Robin Visser, Nov 04 2024

Crossrefs

Cf. A005788, A060564.

Sequence in context: A322015 A285311 A285131 * A270392 A060284 A036275

Adjacent sequences: A110617 A110618 A110619 * A110621 A110622 A110623

Keyword

nonn

Author

Steven Finch, Sep 14 2005

Status

approved