A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is
The Number Of Rational Points On Elliptic Curves Y2 = X3 + A3 On Finite Fields
In this work, we consider the rational points on elliptic curves over finite fields Fp. We give results concerning the number of points Np,a on the elliptic curve y2 ≡ x3 +a3(mod p) according to whether a and x are quadratic residues or non-residues. We use two lemmas to prove the main results first of which gives the list of primes for which -1 is a quadratic residue, and the second is a result from . We get the results in the case where p is a prime congruent to 5 modulo 6, while when p isdoi:10.5281/zenodo.1332804 fatcat:ia4eosjo6jazrilb4zxnf6fqam