This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060564 #28 Feb 16 2025 08:32:44 %S A060564 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, %T A060564 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, %U A060564 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 %N A060564 Number of elliptic curves (up to isogeny) of conductor n. %C A060564 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 %H A060564 J. E. Cremona, <a href="/A060564/b060564.txt">Table of n, a(n) for n = 1..10000</a> %H A060564 J. E. Cremona, <a href="https://johncremona.github.io/ecdata/">Elliptic Curve Data</a> %H A060564 A. Dujella, <a href="https://web.math.pmf.unizg.hr/~duje/tors/rankhist.html">History of elliptic rank records</a> %H A060564 LMFDB, <a href="https://www.lmfdb.org/EllipticCurve/Q/">Elliptic curves over Q</a> %H A060564 F. Richman, <a href="http://math.fau.edu/Richman/elliptic.htm">Elliptic curves</a> [broken link] %H A060564 A. L. Robledo, PlanetMath.org, <a href="http://planetmath.org/encyclopedia/ArithmeticOfEllipticCurves.html">The Arithmetic of Elliptic Curves</a> [broken link] %H A060564 E. Savaş, T. A. Schmidt, and Ç. K. Koç, <a href="https://doi.org/10.1007/3-540-44709-1_13">Generating Elliptic Curves of Prime Order</a>. 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. %H A060564 J. S. Silverman, <a href="http://www.math.brown.edu/~jhs/Presentations/WyomingEllipticCurve.pdf">An Introduction to the Theory of Elliptic Curves</a> %H A060564 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EllipticCurve.html">Elliptic Curve</a> %e A060564 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 %o A060564 (Sage) # Uses Cremona's database of elliptic curves (works for all n < 500000) %o A060564 def a(n): %o A060564 return CremonaDatabase().number_of_isogeny_classes(n) # _Robin Visser_, Nov 04 2024 %Y A060564 Cf. A005788, A110620, A127788. %K A060564 nonn,nice %O A060564 1,26 %A A060564 _N. J. A. Sloane_, Apr 12 2001