Published June 30, 2025 | Version v1
Dataset Open

Frobenious traces for a set of isogeny classes of elliptic curves of conductor up to 10^6

Authors/Creators

  • 1. ROR icon Massachusetts Institute of Technology

Description

This builds on A set of isogeny classes of elliptic curves of conductor up to 10^8. Where only the curves of conductor less than 10^6 were kept, and the column ap was added.
Concretely, the format is N:hash:disc:ainvs:rank:torsion:cm:ap where

  • N is the conductor.
  • hash is an isogeny class invariant (to avoid potential collisions, include N also).
  • disc is the absolute minimal discriminant (divisible by N and supported on the same primes).
  • ainvs is a list of 5 integers [a1,a2,a3,a4,a6] defining the elliptic curve y^2 + a1 xy + a3 y = x^3 + a2 x^2 + a4 x + a6 .
  • rank is the Mordell-Weil rank (assuming GRH, and also BSD in 146 cases)
  • torsionis the torsion subgroup (this probably should be ignored, since this is not an isogeny invariant and the file consists of isogeny class representatives).
  • cm is 0 if the elliptic curve has endomorphism ring Z and otherwise is the discriminant of the imaginary quadratic order isomorphic to End (E_Qbar), one of −3, −4, −7, −8, −12, −16, −19, −27, −28, −43, −67, −163.
  • ap is the list of ap for p < 1000

The file is sorted on N,hash (this key is unique because they are isogeny class representatives).

Files

ECQ6ap1e4.txt

Files (15.9 GB)

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