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 A361661 #56 Apr 12 2023 08:07:12
%S A361661 0,24,752,7600,71520,592192
%N A361661 Number of Q-isomorphism classes of elliptic curves E/Q with good reduction outside the first n prime numbers.
%C A361661 A. Best and B. Matschke performed a heuristic computation which suggests a(6) = 4576128.
%D A361661 N. M. Stephens, The Birch Swinnerton-Dyer Conjecture for Selmer curves of positive rank, Ph.D. Thesis (1965), The University of Manchester.
%H A361661 M. A. Bennett, A. Gherga, and A. Rechnitzer, <a href="https://doi.org/10.1090/mcom/3370">Computing elliptic curves over Q</a>, Math. Comp., 88(317):1341-1390, 2019.
%H A361661 A. J. Best and B. Matschke, <a href="https://github.com/elliptic-curve-data/ec-data-S6">Elliptic curves with good reduction outside {2, 3, 5, 7, 11, 13}</a>.
%H A361661 A. J. Best and B. Matschke, <a href="https://arxiv.org/abs/2007.10535">Elliptic curves with good reduction outside of the first six primes</a>, arXiv:2007.10535 [math.NT], 2020.
%H A361661 F. B. Coghlan, <a href="https://www.proquest.com/openview/451c146777dad63e754d1a3d0f9eb5ee">Elliptic Curves with Conductor N = 2^m 3^n</a>, Ph.D. Thesis (1967), The University of Manchester.
%H A361661 A. P. Ogg, <a href="https://doi.org/10.1017/S0305004100039670">Abelian curves of 2-power conductor</a>, Proc. Cambridge Philos. Soc. 62 (1966), 143-148.
%H A361661 R. von Känel and B. Matschke, <a href="https://arxiv.org/abs/1605.06079">Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture</a>, arXiv:1605.06079 [math.NT], 2016.
%e A361661 For n = 0, Tate proved there are no elliptic curves over Q with good reduction everywhere, so a(0) = 0.
%e A361661 For n = 1, there are a(1) = 24 elliptic curves over Q with good reduction outside 2, classified by Ogg (1966), with j-invariants given in A332545. E.g., a set of 24 Weierstrass equations for these curves can be given as: y^2 = x^3 - 11*x - 14, y^2 = x^3 - 11*x + 14, y^2 = x^3 - x, y^2 = x^3 + 4*x, y^2 = x^3 - 44*x - 112, y^2 = x^3 - 44*x + 112, y^2 = x^3 - 4*x, y^2 = x^3 + x, y^2 = x^3 + x^2 - 9*x + 7, y^2 = x^3 + x^2 + x + 1, y^2 = x^3 + x^2 - 2*x - 2, y^2 = x^3 + x^2 + 3*x - 5, y^2 = x^3 - x^2 - 9*x - 7, y^2 = x^3 - x^2 + x - 1, y^2 = x^3 - x^2 - 2*x + 2, y^2 = x^3 - x^2 + 3*x + 5, y^2 = x^3 + x^2 - 13*x - 21, y^2 = x^3 + x^2 - 3*x + 1, y^2 = x^3 - 2*x, y^2 = x^3 + 8*x, y^2 = x^3 - 8*x, y^2 = x^3 + 2*x, y^2 = x^3 - x^2 - 13*x + 21, y^2 = x^3 - x^2 - 3*x - 1.
%o A361661 (Sage)
%o A361661 def a(n):
%o A361661 S = Primes()[:n]
%o A361661 EC = EllipticCurves_with_good_reduction_outside_S(S)
%o A361661 return len(EC)
%Y A361661 Cf. A332545, A359480.
%K A361661 nonn,more
%O A361661 0,2
%A A361661 _Robin Visser_, Mar 21 2023