Isomorphism classes of elliptic curves over a finite field in some thin families
Isomorphism classes of elliptic curves over a finite field in some thin families
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DOI：
10.4310/mrl.2012.v19.n2.a6
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发表时间：
2012
影响因子：
1
通讯作者：
J. Cilleruelo;I. Shparlinski;Ana Zumalacárregui
中科院分区：
文献类型：
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作者：
J. Cilleruelo;I. Shparlinski;Ana Zumalacárregui
对于素数p和给定的方盒B，我们考虑定义在系数为(r，S)∈B的p元域FP上的所有椭圆曲线Er，S：Y2=X3+RX+S，得到了关于B的大小同构于Fp上一条椭圆曲线的个数的一个非平凡上界，并给出了所表示的不同同构类数的一个最优下界.
For a prime p and a given square box, B, we consider all elliptic curves Er,s : Y 2 = X 3 + rX + s defined over a field Fp of p elements with coefficients (r, s) ∈ B. We obtain a nontrivial upper bound for the number of such curves which are isomorphic to ag iven one overFp, in terms of the size of B. We also give an optimal lower bound on the number of distinct isomorphic classes represented.