A060564 Number of elliptic curves (up to isogeny) of conductor n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 1, 2, 3, 2, 0, 0, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 0, 1, 1, 0, 3, 1, 3, 1, 1, 2, 0, 1, 1, 2, 1, 0, 0, 1, 2, 3, 2, 2, 0, 1, 0, 2, 0, 1, 4

Offset: 1

Author

N. J. A. Sloane, Apr 12 2001

Keywords

• nonn
• nice

Comments

By the modularity of elliptic curves over Q (proved by Breuil-Conrad-Diamond-Taylor), a(n) is equivalently the number of integral normalized weight 2 newforms for Gamma_0(n). - Robin Visser, Nov 04 2024

Examples

			a(11) = 1, as there is exactly one isogeny class of elliptic curves over Q of conductor 11, represented by E : y^2 + y = x^3 - x^2. - _Robin Visser_, Nov 04 2024
		

Links

• J. E. Cremona, Table of n, a(n) for n = 1..10000
• J. E. Cremona, Elliptic Curve Data
• A. Dujella, History of elliptic rank records
• LMFDB, Elliptic curves over Q
• F. Richman, Elliptic curves [broken link]
• A. L. Robledo, PlanetMath.org, The Arithmetic of Elliptic Curves [broken link]
• E. Savaş, T. A. Schmidt, and Ç. K. Koç, Generating Elliptic Curves of Prime Order. In: Koç, Ç.K., Naccache, D., Paar, C. (eds) Cryptographic Hardware and Embedded Systems — CHES 2001. CHES 2001. Lecture Notes in Computer Science, vol 2162. Springer, Berlin, Heidelberg.
• J. S. Silverman, An Introduction to the Theory of Elliptic Curves
• Eric Weisstein's World of Mathematics, Elliptic Curve

Crossrefs

Cf. A005788, A110620, A127788.

Programs

Sage

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