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商洛学院数学与计算机应用学院初等数论课件Chapter 6 Elliptic Curves
商洛学院数学与计算机应用学院 初等数论 课件 Chapter 6 Elliptic Curves
2017/4/7
商洛学院数学与计算机应用学院初等数论课件Chapter 6 Elliptic Curves.
A Cohen-Lenstra phenomenon for elliptic curves
A Cohen-Lenstra phenomenon elliptic curves Number Theory
2012/6/29
Given an elliptic curve $E$ and a finite Abelian group $G$, we consider the problem of counting the number of primes $p$ for which the group of points modulo $p$ is isomorphic to $G$. Under a certain ...
On Zagier's conjecture for base extensions of elliptic curves
Zagier's conjecture base extensions of elliptic curves Number Theory
2012/4/18
Let E be an elliptic curve over Q, and let F be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjecture for L(E/F,2), whe...
On the Surjectivity of Galois Representations Associated to Elliptic Curves over Number Fields
Surjectivity Galois Representations Elliptic Curves over Number Fields Number Theory
2012/4/17
Given an elliptic curve $E$ over a number field $K$, the $\ell$-torsion points $E[\ell]$ of $E$ define a Galois representation $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$. A famous theorem of Serre states t...
Non-existence of elliptic curves with everywhere good reduction over some real quadratic fields
Non-existence of elliptic curves quadratic fields Number Theory
2011/9/19
Abstract: We prove the non-existence of elliptic curves having good reduction everywhere over some real quadratic fields.
Explicit n-descent on elliptic curves. III. Algorithms
Explicit n-descent elliptic curves Algorithms Number Theory
2011/9/14
Abstract: This is the third in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n. The metho...
Identifying supersingular elliptic curves
Identifying supersingular elliptic curves Number Theory
2011/8/26
Abstract: Given an elliptic curve E over a field of characteristic p, we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of several existing alg...
A mean value formula for elliptic curves
elliptic curves Weierstrass ℘ -function point multiplication division polynomial
2011/8/24
Abstract: It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its ...
Heuristics on pairing-friendly elliptic curves
Elliptic curves finite fields pairing-based cryptography
2011/8/23
Abstract: We present a heuristic asymptotic formula as $x\to \infty$ for the number of pairing-friendly elliptic curves with fixed embedding degree $k\geq 3$, with fixed discriminant, with rho-value b...