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Some remarks on the number of points on elliptic curves over finite prime field
Published online by Cambridge University Press: 17 April 2009
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Let p ≥ 5 be a prime and for a, b ε p, let Ea, b denote the elliptic curve over p with equation y2 = x3 + ax + b. As usual define the trace of Frobenius ap, a, b by
We use elementary facts about exponential sums and known results about binary quadratic forms over finite fields to evaluate the sums and
for primes p in various congruence classes.
As an example of our results, we prove the following: Let p ≡ 5 (mod 6) be prime and let b ε *p. Then
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 75 , Issue 1 , February 2007 , pp. 135 - 149
- Copyright
- Copyright © Australian Mathematical Society 2007
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