Complex multiplication tests for elliptic curves - Charles - 2004 () Citation Context ...nd other aspects of algorithmic number theory [6]. Motivated by this, one might seek an algorithm for determining whether a given elliptic curve E over a number field K has complex multiplication. In =-...
Elliptic curvesroot numbercomplex multiplicationquadratic twistsLetE/Fbe an elliptic curve defined over a number fieldF. Suppose thatEhas complex multiplication overF, i.e.EndF(E)is an imaginary quadratic field. With the aid of CM theory, we find elliptic curves whose quadratic twists have a ...
1) complex multiplication 虚数乘法 1. Whencomplex multiplication(CM) is used to create elliptic curves over F_p,the ring of complex quadratic field is only used. 利用虚数乘法(Com p lex M u ltip lication,CM)生成Fp上的椭圆曲线,通常只使用虚二次域的最大整环。
IfEdoes not have complex multiplication, then\mathcal {O}=\mathbb {Z}. In this case, we are almost in the setting of [13]. For this reason, we call this paper “sequences associated to curves with complex multiplication”. In any case, even whenEdoes not have CM, Theorem1.8and Corol...
On units related to the arithmetic of elliptic curves with complex multiplication Let C be an elliptic curve defined over Q. Let p be a prime where C has good reduction. By definition, p is anomalous for C if the Hasse invariant at p is ... F Hajir - 《Archiv Der Mathematik》 被引...
In this article, we address a question along this line for elliptic curves that have complex multiplication defined over number fields. So long as we use diagonal rational \({\mathcal{N}=(2,2)}\) superconformal field theories for the string-theory realizations of the elliptic curves, the ...
Arithmetic on Elliptic Curves with Complex Multiplication 作者:B.H. Gross 出版社:Springer 出版年:1980-3-18 页数:95 定价:USD 39.95 装帧:Paperback ISBN:9783540097433 豆瓣评分 目前无人评价 评价: 写笔记 写书评 加入购书单 分享到
On the 2-part of the Birch–Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of ?(?7) On the2-part of the Birch–Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of(7)... T Yoshida - 《Inte...
The paper uses Iwasawa theory at the prime p=2 to prove non‐vanishing theorems for the value at s=1 of the complex L ‐series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field K=Q(q) , where q is any prime ≡7mod8 . Our ...
Lecture Notes in Mathematics Arithmetic on Elliptic Curves with Complex Multiplication The Conjecture of Birch and Swinnerton-Dyer relates an analytic invariant of an elliptic curve -- the value of the L-function, to an algebraic invariant of the curve -- the order of the Tate--Shafarevich group...