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2016-08-18 18:19:36 +0200 received badge  Nice Answer (source)
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2015-04-30 08:19:52 +0200 answered a question Listing a few points in an elliptic curve

See the SageMath reference manual for elliptic curves over finite fields.

Here there are some examples that may help:

sage: k = GF(next_prime(7^5))
sage: E = EllipticCurve(k,[2,4])
sage: P = E.random_element(); P
(16740 : 12486 : 1)