Cremona's database of all elliptic curves over Q of conductor up to 500,000, with extensive arithmetic data for each curve.

John Cremona

Tables of all 3,064,705 elliptic curves over Q of conductor up to 500,000 (in 2,164,260 isogeny classes), giving for each curve its rank, generators, torsion, Hecke eigenvalues, isogeny matrices, BSD invariants and analytic order of Sha, modular parametrization degrees, integral points, optimality and Manin constants, images of mod-p and 2-adic Galois representations, and torsion growth in number fields. This data has been incorporated into the LMFDB, which provides a more sophisticated web interface for it.

References

  • J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, 1992 (2nd edition 1997)
  • J. E. Cremona, The elliptic curve database for conductors to 130000, in Algorithmic Number Theory (ANTS VII), Lecture Notes in Comput. Sci. 4076, Springer, 2006