I would guess not. People just tried computing the MW group of $y^2 = x^3 + k$ for all positive $k<10000$, and succeeded, except for $k=7823$, which required new methods to complete.

Hi -- purple sage didn't work due to lack of time. Regarding dumping useful code on us, that we have to understand and get up to snuff for inclusion, if we had more time and bandwidth, then we would make that easy. However, we don't -- I have almost not grant support, and almost all effort is researchers in their spare time. Maybe if we someday have funding...

Just a remark that Hao is my Ph.D. student, and one of the motivations for him doing the above is computation of things like the Mazur--Swinnerton-Dyer critical subgroup of E(Q)...

And I made the database_odlyzko_zeta package (which is pre-installed into cloud.sagemath.com) using files from dtc.umn.edu/~odlyzko/zeta_tables