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2014 Explicit points on the Legendre curve III
Douglas Ulmer
Algebra Number Theory 8(10): 2471-2522 (2014). DOI: 10.2140/ant.2014.8.2471

Abstract

We continue our study of the Legendre elliptic curve y2=x(x+1)(x+t) over function fields Kd=Fp(μd,t1d). When d=pf+1, we have previously exhibited explicit points generating a subgroup VdE(Kd) of rank d2 and of finite, p-power index. We also proved the finiteness of Ш(EKd) and a class number formula: [E(Kd):Vd]2=|Ш(EKd)|. In this paper, we compute E(Kd)Vd and Ш(EKd) explicitly as modules over p[Gal(KdFp(t))].

An errata was posted on 31 May 2017 in an online supplement.

Citation

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Douglas Ulmer. "Explicit points on the Legendre curve III." Algebra Number Theory 8 (10) 2471 - 2522, 2014. https://doi.org/10.2140/ant.2014.8.2471

Information

Received: 26 June 2014; Revised: 20 October 2014; Accepted: 23 November 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1325.11057
MathSciNet: MR3298546
Digital Object Identifier: 10.2140/ant.2014.8.2471

Subjects:
Primary: 11G05, 14G05
Secondary: 11G40, 14K15

Rights: Copyright © 2014 Mathematical Sciences Publishers

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