choy valerie on Wed, 15 May 2013 11:08:19 +0200


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ellap problem


Hi,

I was trying to compute the cardinality of a 512-bit elliptic curve. For example, for y^2 = x^3 + a4.x + a6 mod p where

p=10566623376041669505825220895462627801380145726624712771836144280024219722297939525451022774579043146020265329009462778097121538072213487555318041328039599
a4=6557325753041215216697541661243177462316789827714644669153173743634615853451990973713919498189870050066222585898470391225455349541996119434962754618249308
a6=3887529832007272230349363633177495741990999092935596186265775681498612008751646149414901742385996951003068331698140100902826619262789957720578797201032523

When I tried to compute the order directly using GP with:

sage: E = gp.ellinit([0,0,0,a4,a6])
sage: ap = E.ellap(p)

I encountered the error:

*** at top-level: sage[9] = ellap(sage[7],sage[8]
***                                   ^----------------------
*** ellap: not enough modular polynomials

May I know how to resolve this problem? Any help is greatly appreciated!

Valerie