三自由度椭圆曲线族的新发现和研究
首发时间:2019-06-10
摘要:众所周知,Tate 曲线族,(形如 1.4 ) 具有2个自由度 c,b. 本文对形如 1.5的曲线族进行了研究,该曲线族具有 3个自由度 m、k、q. 研究发现此曲线与 Tate 族曲线一样,具有 Z4-Z10,Z12 的挠群结构,而且 Tate 族曲线族只是本曲线族的一个子族 (当 k= -1 同时 m=1-c 时,本曲线族就是 Tate 曲线族.) ?????
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The new discovery and study of three degrees of freedom elliptic curve family
Abstract:As is known to all, Tate family of curves, like (1.4), has two degrees of freedom c, b. This paper studies another family of curves, This family of curves which form such as (1.5), with three degrees of freedom m, k, q It is found that this curve is the same as that of the Tate family, with Z4-Z10,Z12 torsion group structure, and the Tate family is only a subfamily of this curve family. (when k=1 and m=1-c, the curve family is the Tate curve family).
Keywords: algebra geometry, elliptic curve, torsion group, torsion group calculation.
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