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

24, 752, 280, 288, 232, 336, 256, 336, 256, 296, 280, 240, 176, 168, 136, 296, 304, 176, 112, 288, 136, 304, 176, 192, 152, 216, 104, 240, 160, 144, 280, 160, 152, 168, 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

Offset: 1

Author

Robin Visser, Mar 31 2023

Keywords

• nonn

Comments

R. von Känel and B. Matschke conjecture that a(n) <= a(2) = 752 for all n.

Examples

			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.
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).
		

References

• N. M. Stephens, The Birch Swinnerton-Dyer Conjecture for Selmer curves of positive rank, Ph.D. Thesis (1965), The University of Manchester.

Links

• F. B. Coghlan, Elliptic Curves with Conductor N = 2^m 3^n, Ph.D. Thesis (1967), The University of Manchester.
• J. E. Cremona and M. P. Lingham, Finding all elliptic curves with good reduction outside a given set of primes, Experiment. Math. 16 (2007), no. 3, 303-312.
• A. P. Ogg, Abelian curves of 2-power conductor, Proc. Cambridge Philos. Soc. 62 (1966), 143-148.
• R. von Känel and B. Matschke, List of all rational elliptic curves with good reduction outside {2, p} up to Q-isomorphisms, 2015.

Crossrefs

Cf. A332545, A361661.

Programs

Sage

# This is very slow!
def a(n):
    S = list(set([2, Primes()[n-1]]))
    EC = EllipticCurves_with_good_reduction_outside_S(S)
    return len(EC)