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

Author

Steven Finch, Sep 14 2005

Keywords

• nonn

Examples

			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.
		

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.

Crossrefs

Cf. A005788, A060564.

Programs

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