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.
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页数：26
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