J. L. Lehman, Rational po√ints on elliptic curves with complex multiplication by the ring of integers in Q( -7), J. Number Theory 27 (1987), 253-272J. L. Lehman, Rational points on elliptic curves with complex
root 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 constant root ...
In the last fifteen years the Iwasawa theory has been applied with remarkable success to elliptic curves with complex multiplication. A clear yet general exposition of this theory is presented in this book. Following a chapter on formal groups and local units, the p-adic L functions of Manin-...
We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show – under additional congruence assumptions on the CM order – that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the ...
On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields Nagoya Math. J, 43 (1971), pp. 199-208 View in ScopusGoogle Scholar [4] G. Shimura On the zeta-function of an abelian variety with complex multiplication Ann. Math, 94 (1971), pp. 504...
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 写笔记 写书评 加入购书单 分享到 推荐 我要写书评 Arithmetic on Elliptic Curves with Complex Multiplication的书评 ···(全部 0 条) 论坛· ...
K. Rubin. Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication. Invent. Math., 89(3):527–559, 1987. Article MathSciNet MATH Google Scholar K. Rubin. The “main conjectures” of Iwasawa theory for imaginary quadratic fields. Invent. Math., 103(1):25–68...
“sequences associated to curves with complex multiplication”. in any case, even when e does not have cm, theorem 1.8 and corollary 7.5 are new and generalize the work in [ 13 ]. the paper is organized as follows. in sect. 2 , we give some preliminary definitions on elliptic curves. ...
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 curves with complex multiplication (denoted CM). His proof uses class field theoretical properties of CM elliptic curves and the large sieve for number fields in the form of a num- ber field version of the Bombieri-Vinogradov Theorem. In 1987 [RM87] he also demonstrated uncondi...