Add intrinsic subgroup order to elliptic curve data and search options

[jacobjpg]

The intrinsic subgroup is defined in arXiv:2512.00787. Adding computed values of the order of the intrinsic subgroup for elliptic curves over Q.

[JohnCremona]

I do not remember seeing any discussion of whether or not the new column 'intrinsic_torsion' should be added to the ec_curvedata column. I don't think that an index on this quantity has been added, which it should be before allowing searching on it.

The cited paper does not (as far as I can tell) include an algorithm for computing this number (which appears to be an integer in the range 1..5) for an elliptic curve over Q. Is the algorithm available anywhere? It will need to be run on onay new curves added to the database in future.

[AndrewVSutherland]

@jacobjpg worked out a (surprisingly simple) algorithm for computing this for any E/Q in Sage and is in the process of settingup a public repo for the code. I just added an index on intrinsic_torsion.

[AndrewVSutherland]

In principle it should be straight-forward to extend this to ECNF, but the algorithm will be a bit more complicated; I think it makes sense to get everything in place for ECQ first.