Spanning the isogeny class of a power of an elliptic curve
Spanning the isogeny class of a power of an elliptic curve
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跨越椭圆曲线幂的同源类
DOI：
10.1090/mcom/3672
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Damien Robert
中科院分区：
文献类型：
--
作者：
M. Kirschmer;Fabien Narbonne;C. Ritzenthaler;Damien Robert
让
E
E
是有限域上的普通椭圆曲线，
G
G
是一个正整数。在某些技术假设下，我们给出了一个算法，使主极化阿贝尔簇的同构类在
E
G
E^g
.该品种首先描述为厄米特格（不一定是最大的）二次订单，然后在几何方面的代数θ零点。我们还展示了如何代数计算西格尔模块化的形式，甚至重量作为多项式的θ常数的仿射电梯的θ零点的仔细选择。然后，我们利用这些结果给出了一个代数计算Serre的阻塞的主要极化阿贝尔三重同构到
E
3
E^3
和伊古萨模形式的维度
4
4
.我们说明我们的算法与曲线的例子，在有限域上有许多合理的点。
Let
E
E
be an ordinary elliptic curve over a finite field and
g
g
be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of
E
g
E^g
. The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to
E
3
E^3
and of the Igusa modular form in dimension
4
4
. We illustrate our algorithms with examples of curves with many rational points over finite fields.
皮卡德曲线的逆雅可比算法
影响因子：
0.8
作者：
Lario, Joan-C.;Somoza, Anna;Vincent, Christelle
通讯作者：
Vincent, Christelle