Remarks on the Schoof-Elkies-Atkin algorithm
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منابع مشابه
Remarks on the Schoof-Elkies-Atkin algorithm
Schoof’s algorithm computes the number m of points on an elliptic curve E defined over a finite field Fq. Schoof determines m modulo small primes ` using the characteristic equation of the Frobenius of E and polynomials of degree O(`2). With the works of Elkies and Atkin, we have just to compute, when ` is a “good” prime, an eigenvalue of the Frobenius using polynomials of degree O(`). In this ...
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Let A be an abelian variety over a number field K. If P and Q are K-rational points of A such that the order of the (mod p) reduction of Q divides the order of the (mod p) reduction of Q for almost all primes (mod p), then there exists a K-endomorphism φ of A and a positive integer k such that kQ = φ(P). In this paper, we solve the support problem for abelian varieties over number fields, thus ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1998
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-98-00962-4