Journal ArticleDOI
Lectures on elliptic curves, London Mathematical Society Student Texts 24, by J. W. S. Cassels. Pp 137. £13-95 (paper) £27-95 (hard). 1991. ISBN 0-521-42530-1, -41517-9. (Cambridge University Press)
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This article is published in The Mathematical Gazette.The article was published on 1995-03-01. It has received 37 citations till now.read more
Citations
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Book ChapterDOI
Hessian Elliptic Curves and Side-Channel Attacks
TL;DR: This paper investigates the Hessian parameterization of an elliptic curve as a step towards resistance against side-channel attacks in the context of elliptic Curve cryptography.
Journal Article
Topological Strings And (Almost) Modular Forms
TL;DR: Aganagic et al. as discussed by the authors showed that the genus g topological string amplitude is either a holomorphic quasi-modular form or an almost holomorphic modular form of weight 0 under Γ.
Journal ArticleDOI
Mahler's Measure and Special Values of L-functions
TL;DR: Some examples for which it appear that log M(P(x, y) = rL'(E, 0), where E is an elliptic curve and r is a rational number, often either an integer or the reciprocal of an integer.
Journal ArticleDOI
Efficient solution of rational conics
John Cremona,David J. Rusin +1 more
TL;DR: This work presents efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions and shows that no integer factorization is required.
Journal ArticleDOI
Computing all integer solutions of a genus 1 equation
Roel Stroeker,Nikos Tzanakis +1 more
TL;DR: The elliptic logarithm method has been applied with great success to the problem of computing all integer solutions of equations of degree 3 and 4 defining elliptic curves as mentioned in this paper.
References
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Journal ArticleDOI
Topological Strings and (Almost) Modular Forms
TL;DR: The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Γ, generated by monodromies of the periods of X as mentioned in this paper.
Book ChapterDOI
Hessian Elliptic Curves and Side-Channel Attacks
TL;DR: This paper investigates the Hessian parameterization of an elliptic curve as a step towards resistance against side-channel attacks in the context of elliptic Curve cryptography.
Journal ArticleDOI
Mahler's Measure and Special Values of L-functions
TL;DR: Some examples for which it appear that log M(P(x, y) = rL'(E, 0), where E is an elliptic curve and r is a rational number, often either an integer or the reciprocal of an integer.
Journal ArticleDOI
Efficient solution of rational conics
John Cremona,David J. Rusin +1 more
TL;DR: This work presents efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions and shows that no integer factorization is required.
Journal ArticleDOI
Functional equations for Mahler measures of genus-one curves
Matilde Lalín,Mathew D. Rogers +1 more
TL;DR: In this article, the authors established functional equations for Mahler measures of families of genus-one polynomials and proved identities between Mahler measure conjectured by Boyd, Rodriguez Villegas, Bertin, Zagier, and Stienstra.