منابع مشابه
Computing Canonical Heights on Elliptic Curves in Quasi-linear Time
We introduce an algorithm that can be used to compute the canonical height of a point on an elliptic curve over the rationals in quasi-linear time. As in most previous algorithms, we decompose the difference between the canonical and the naive height into an archimedean and a non-archimedean term. Our main contribution is an algorithm for the computation of the non-archimedean term that require...
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In 2006, Mazur, Stein, and Tate [4] gave an algorithm for computing p-adic heights on elliptic curves E over Q for good, ordinary primes p ≥ 5. Their work makes essential use of Kedlaya’s algorithm [3], where the action of Frobenius is computed on a certain basis of the first de Rham cohomology of E, with E given by a “short” Weierstrass model. Kedlaya’s algorithm requires that the working mode...
متن کاملComputing rational points on rank 1 elliptic curves via L-series and canonical heights
Let E/Q be an elliptic curve of rank 1. We describe an algorithm which uses the value of L′(E, 1) and the theory of canonical heghts to efficiently search for points in E(Q) and E(ZS). For rank 1 elliptic curves E/Q of moderately large conductor (say on the order of 107 to 1010) and with a generator having moderately large canonical height (say between 13 and 50), our algorithm is the first pra...
متن کاملCANONICAL HEIGHTS ON ELLIPTIC CURVES IN CHARACTERISTIC p
Let k = Fq(t) be the rational function field with finite constant field and characteristic p ≥ 3, and let K/k be a finite separable extension. For a fixed place v of k and an elliptic curveE/K which has ordinary reduction at all places ofK extending v, we consider a canonical height pairing 〈 , 〉v : E(K ) × E(K) → C v which is symmetric, bilinear and Galois equivariant. The pairing 〈 , 〉∞ for t...
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We introduce an l-adic algorithm to efficiently determine the group of rational torsion points on an elliptic curve. We also make a conjecture about the discriminant of the m-division polynomial of an elliptic curve.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1988
ISSN: 0025-5718
DOI: 10.2307/2008597