Bill Allombert on Mon, 17 Nov 2014 17:24:15 +0100

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New GP functions for modular polynomials

Dear PARI developers,

We have recently added three new GP functions in PARI GIT 2.8, implemented
by Hamish Ivey-Law, using Sutherland algorithm:

polmodular(l): return the canonical modular polynomial of level l prime.
(unfortunately limited to l<=31 in 32bit)

polclass(D): return the Hilbert class polynomial for the imaginary order.

ellissupersingular(E): test whether E is supersingular (faster than ellap).

Also this was the last missing piece for polynomial time point
counting function for elliptic curve over GF(p^n) (ellcard).
We use 5 different algorithms depending on n and p:

- if p==2,        we use Satoh-Mestre-Harley AGM algorithm 
- if p==3,5,7,13  we use Satoh-Harley-Kohel algorithm.

- if n<=p/2,      we use SEA (Joux-Lercier variant).
- if p/2<n<7/10*p we use Kedlaya algorith (following Gaudry-Gürel).
- if n>=7/10*p,   we use Satoh-Mestre-Harley algorithm (which requires 

So, please test (in 64bit).