Published June 30, 2025
| Version v1
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Frobenious traces for a set of isogeny classes of elliptic curves of conductor up to 10^6
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
Nis the conductor.hashis an isogeny class invariant (to avoid potential collisions, includeNalso).discis the absolute minimal discriminant (divisible byNand supported on the same primes).ainvsis 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 .rankis 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).cmis 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.apis 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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