Exponents of Modular Reductions of Families of Elliptic Curves
نویسنده
چکیده
For a basic background on elliptic curves, we refer to [11]. For a prime p > 3, we denote by Fp the finite field of p elements, which we identify with the set of integers {0,±1, . . . ,±(p− 1)/2}. When p ∤ 4a+27b, the set Ea,b(Fp), consisting of the Fp-rational points of Ea,b together with a point at infinity O, forms an abelian group under an appropriate composition rule called addition, and the number of elements in the group Ea,b(Fp) satisfies the Hasse bound :
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