Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences
نویسنده
چکیده
Let F (x, y) = ax + bxy + cy be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = −1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y = ax + bx + cx be an elliptic curve over Fp and let CF : ax + bx + cx ≡ 0(mod p) be the cubic congruence corresponding to F . In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences. Keywords—Binary quadratic form, elliptic curves, cubic congruence.
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