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

1,1

Comments

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

References

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

Links

Table of n, a(n) for n=1..59.

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.

Example

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).

Prog

(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)

Crossrefs

Cf. A332545, A361661.

Sequence in context: A062528 A175604 A283873 * A361661 A269147 A269209

Adjacent sequences: A359477 A359478 A359479 * A359481 A359482 A359483

Keyword

nonn

Author

Robin Visser, Mar 31 2023

Status

approved