A remark on the group structure of elliptic curves in towers of finite fields
A remark on the group structure of elliptic curves in towers of finite fields
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有限域塔中椭圆曲线群结构的评述
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发表时间：
2018
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通讯作者：
J. Cullinan
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作者：
J. Cullinan
设L是奇素数，F是具有不同于L的特征的有限域，A和B是定义在F上的L同源椭圆曲线.研究了A(L)和B(L)的群结构在有限扩张L/F中的变化，证明了如果群A(F)和B(F)的基数可被L整除，且如果A(F)和B(F)同构，则对F的所有有限扩张L，A(L)和B(L)也是同构的.
Let l be an odd prime, let F be a finite field of characteristic different from l and let A and B be l-isogenous elliptic curves defined over F. We study how the group structures of A(L) and B(L) vary in finite extensions L/F and prove that if the cardinality of the groups A(F) and B(F) are divisible by l and if A(F) and B(F) are isomorphic, then so are A(L) and B(L) for all finite extensions L of F.