Constructing all genus 2 curves with supersingular Jacobian

被引：1

作者：

Pieper, Andreas ^{[1
]}

机构：

[1] Univ Ulm, Inst Algebra & Zahlentheorie, Helmholtzstr 18, D-89081 Ulm, Germany

来源：

RESEARCH IN NUMBER THEORY | 2022年 / 8卷 / 02期

关键词：

D O I：

10.1007/s40993-022-00330-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

L. Moret-Bailly constructed families C -> P-1 of genus 2 curves with supersingular Jacobian. In this paper we first classify the reducible fibers of a Moret-Bailly family using linear algebra over a quaternion algebra. The main result is an algorithm that exploits properties of two reducible fibers to compute a hyperelliptic model for any irreducible fiber of a Moret-Bailly family.

引用

页数：26

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