FILENAMES: a.000 -- curves up to conductor 100000 a.001 -- curves from conductor 100000 to 200000 ... a.n -- curves from conductor n*10^5 to (n+1)*10^5 (up to 10^8) p.00 -- curves up to 10^8 with prime conductor ... p.n -- curves between n*10^8 and (n+1)*10^8 with prime conductor ... p.99 -- finishes at 10^10 prime conductor FORMAT OF a FILES: A group as follows for each isogeny class. conductor [ordered_prime_divisors_of_conductor] rank L^(rank)(1)/rank! isogeny_number ??modular_degree a_invariants ord(Delta) analytic_sha torsion_subgroup .... a_invariants ord(Delta) analytic_sha torsion_subgroup COMMENTS: isogeny_number - This number is the longest degree of a chain of isogenies between non-isomorphic curves. For example, a 12 means the isogeny class contains a curve which possesses a 12-isogeny. modular_degree - The modular degree of the optimal quotient of J_0(N). The star means that the curve of minimal Faltings height is not J0-optimal. The plus indicates that the minimal Faltings height curve is a minimal quadratic twist. torsion_subgroup - n or nx, where n means Z/nZ and nx means Z/nZ x Z/2Z (only used when n even). ord(Delta) - Surrounded in square or round brackets: * square means that Delta is positive and * round brackets mean that Delta is negative. The numbers listed are the valuations of Delta at each prime dividing the level, in order. analytic_sha - analytic order of Sha