cp's OEIS Frontend

A359480 Number of Q-isomorphism classes of elliptic curves E/Q with good reduction away from 2 and prime(n).

%I A359480 #19 Jun 23 2023 03:30:53
%S A359480 24,752,280,288,232,336,256,336,256,296,280,240,176,168,136,296,304,
%T A359480 176,112,288,136,304,176,192,152,216,104,240,160,144,280,160,152,168,
%U A359480 112,128,136,232,144,184,128,152,80,88,112,112,112,280,112,288,160,120,168,112,224,112,120,112,136
%N A359480 Number of Q-isomorphism classes of elliptic curves E/Q with good reduction away from 2 and prime(n).
%C A359480 R. von Känel and B. Matschke conjecture that a(n) <= a(2) = 752 for all n.
%D A359480 N. M. Stephens, The Birch Swinnerton-Dyer Conjecture for Selmer curves of positive rank, Ph.D. Thesis (1965), The University of Manchester.
%H A359480 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 A359480 J. E. Cremona and M. P. Lingham, <a href="https://projecteuclid.org/journals/experimental-mathematics/volume-16/issue-3/Finding-All-Elliptic-Curves-with-Good-Reduction-Outside-a-Given/em/1204928531.full">Finding all elliptic curves with good reduction outside a given set of primes</a>, Experiment. Math. 16 (2007), no. 3, 303-312.
%H A359480 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 A359480 R. von Känel and B. Matschke, <a href="https://github.com/bmatschke/solving-classical-diophantine-equations/blob/master/elliptic-curve-database/curves__S_2_p_pMax250.txt">List of all rational elliptic curves with good reduction outside {2, p} up to Q-isomorphisms</a>, 2015.
%e A359480 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 A359480 For n = 2, there are a(2) = 752 elliptic curves over Q with good reduction outside {2,3}, classified independently by Coghlan (1967) and Stephens (1965).
%o A359480 (Sage) # This is very slow!
%o A359480 def a(n):
%o A359480     S = list(set([2, Primes()[n-1]]))
%o A359480     EC = EllipticCurves_with_good_reduction_outside_S(S)
%o A359480     return len(EC)
%Y A359480 Cf. A332545, A361661.
%K A359480 nonn
%O A359480 1,1
%A A359480 _Robin Visser_, Mar 31 2023