Alasdair McAndrew on Thu, 28 Jun 2012 02:18:06 +0200

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Elliptic curves over GF(p)?

 To: pariusers <pariusers@pari.math.ubordeaux.fr>
 Subject: Elliptic curves over GF(p)?
 From: Alasdair McAndrew <amca01@gmail.com>
 Date: Thu, 28 Jun 2012 10:17:54 +1000
 Deliverydate: Thu, 28 Jun 2012 02:18:16 +0200
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Hello,
I want to do some simple computation on elliptic curves of the form y^2 = x^3 + ax +b (mod p), where p is prime (of at least 32 bits) . My needs are simple: define such a curve, find its cardinality, find a generator (if the cardinality is prime) or a point of high order, and in general perform arithmetic on the curve: addition, order, etc. Can libpari manage all of this? The manual is fairly sparse on elliptic curves, and it's not clear to me, as a beginner, whether Pari supports elliptic curves over finite fields GF(p).
Thanks very much!
cheers,
Alasdair