Elliptic curvesFunction fieldsGalois representationsIf F is a global function field of characteristic p > 3, we employ Tate's theory of analytic uniformization to give an alternative proof of a theorem of Igusa describing the image of the natural Galois representation on torsion points of non-iso...
We prove that there are only finitely many complex numbers $a$ and $b$ with $4a^3+27b^2\not=0$ such that the three points $(1,*),(2,*),$ and $(3,*)$ are simultaneously torsion on the elliptic curve defined in Weierstrass form by $y^2=x^3+ax+b$. This give
Lozano-Robledo, Á. On the field of definition ofp-torsion points on elliptic curves over the rationals.Math. Ann.357, 279–305 (2013). https://doi.org/10.1007/s00208-013-0906-5 Download citation Received18 December 2011 Revised16 December 2012 ...
Computing torsion points on curves - Poonen () Citation Context ...cal liftings have been used in many applications, such as counting rational points in ordinary elliptic curves, as in Satoh’s [Sat00], counting torsion points of curves of genus g ≥ 2, as in Poonen’s =-=[Poo01]-=...
Some remarks on torsion in elliptic curves - Kamienny - 1995 () Citation Context ...e classified all the cases and hence reduced Euler’s problem to a question of ranks. In [6], Parshin obtaines an inequality to give an effective bound for the height of rational points on a curve. In...
LetE/Fdenote an elliptic curve defined over a number fieldF. Then the Mordell–Weil theorem states that the abelian groupE(F)ofF-rational points onEis finitely generated. In particular, one has a decompositionE(F)≅Zr(E,F)⊕E(F)[tors]whereE(F)[tors]is itstorsion subgroup over F.In...
1.5.1 Elliptic curves, torsion points, and linear automorphisms Theorem 1.1 describes the number of automorphisms of a group of the form , in case that the matrix is a Hessian determinantal representation of an elliptic curve, in terms of the numbers of such automorphisms that induce automorphisms...
Torsion points on elliptic curves defined over quadratic fields CiteSeerX - Scientific documents that cite the following paper: torsion points on elliptic curves defined over quadratic fields MA Kenku,F Momose - 《Nagoya Mathematical Journal》 被引量: 217发表: 1984年 Torsion groups of elliptic ...
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Let $A$ be an elliptic curve over $\\Q$ of square free conductor $N$. We prove that if $A$ has a rational torsion point of prime order $r$ such that $r$ does not divide $6N$, then $r$ divides the order of the cuspidal subgroup of $J_0(N)$....