The set of K-rational points on an elliptic curve, E, are known to form a finitely generated abelian group. My results are of interest when trying to find the rank of this group, which in general is a hard problem. The Selmer group of E,S(E/K), can be used to give a bound on...
This classif i cation is achieved by showing that the inf i nity partof any elliptic curve over Z/p e Z is a Z/p e Z-torsor.As a f i rst consequence, when E(Z/NZ) is a p-group, we provide an explicitand sharp bound on its rank. As a second consequence, when N = p e ...
英语 翻译Elliptic Curve Group Over GF(P) ECP缩写是椭圆曲线在火焰杯(P)的意思,ECP全写Elliptic Curve Group Over GF(P)。 ECP缩写可能还有其它意思,请根据自身行业、属性核对选择ECP正确的英文缩写及全写。 参考资料: 1.百度翻译:椭圆曲线在火焰杯(P) 2.有道翻译:椭圆曲线在火焰杯(P)获...
We study the group of birational transformations of the plane that fix (each point of) a curve of geometric genus 1. A precise description of the finite elements is given; it is shown in particular that the order is at most 6, and that if the group conta
We present examples of high rank elliptic curves with a given torsion group which set the current rank records for most of the torsion groups. In particular, we show that for each possible torsion group, except maybe for , there exists an elliptic curve over some quadratic field with this ...
43 Adversarial training through the lens of optimal transport 1:16:40 Central Limit Theorems in Analytic Number Theory 48:39 Kantorovich operators and their ergodic properties 1:02:06 L-Functions of Elliptic Curves Modulo Integers 49:33 The Bootstrap Learning Algorithm 20:49 A logarithmic ...
Then, E(Q) has the structure of a finitely generated abelian group (by the Mordell–Weil theorem [50]), i.e., E(Q)=Zr⊕E(Q)tor. Here r∈Z≥0 is called the (algebraic) rank of E, and E(Q)tor is a finite abelian group. Computing the rank of a general elliptic curve is ...
Let E be an elliptic curve over Q and be an odd prime. Also, let K be a number field and assume that E has a semi-stable reduction at . Under certain assu... B Cha - 《Journal of Number Theory》 被引量: 22发表: 2005年 The Tate-Shafarevich Group for Elliptic Curves with Complex...
Shanks's baby-step-giant-step algorithm to count the order of the group of points of an elliptic curve over a finite prime field is described. The algorithm's improvements are also discussed. The first one is based on Mestre's theorem. The second improvement is based on the Sutherland's ...
In this note we discuss techniques for determining the automorphism group of a genus $g$ hyperelliptic curve $\X_g$ defined over an algebraically closed field $k$ of characteristic zero. The first technique uses the classical $GL_2 (k)$-invariants of binary forms. This is a practical meth...