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math.NT2014
Isogeny graphs with maximal real multiplication
Sorina Ionica, Emmanuel Thomé
An isogeny graph is a graph whose vertices are principally polarized abelian varieties and whose edges are isogenies between these varieties. In his thesis, Kohel described the str…
math.NT2012★ 12 cited
Root optimization of polynomials in the number field sieve
Shi Bai, Richard P. Brent, Emmanuel Thomé
The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. T…
math.NT2010★ 23 cited
Visualizing elements of Sha[3] in genus 2 jacobians
Nils Bruin, Sander R. Dahmen
Mazur proved that any element xi of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in the sense…