Isogenies of Elliptic Curves Over Function Fields

被引：2

作者：

Griffon, Richard ^{[1
]}

Pazuki, Fabien ^{[2
]}

机构：

[1] Univ Basel, Dept Math, Spiegelgasse 1, CH-4051 Basel, Switzerland

[2] Univ Copenhagen, Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen, Denmark

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 19期

基金：

瑞士国家科学基金会;

关键词：

DISCRIMINANT; THEOREM;

D O I：

10.1093/imrn/rnab033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove two theorems concerning isogenies of elliptic curves over function fields. The first one describes the variation of the height of the j-invariant in an isogeny class. The second one is an "isogeny estimate," providing an explicit bound on the degree of a minimal isogeny between two isogenous elliptic curves. We also give several corollaries of these two results.

引用

页码：14697 / 14740

页数：44

共 34 条

[1] Torsion points on elliptic curves over function fields and a theorem of Igusa [J].

Bandini, Andrea ;

Longhi, Ignazio ;

Vigni, Stefano .

EXPOSITIONES MATHEMATICAE, 2009, 27 (03) :175-209

[2]

Bosch S., 1990, NERON MODELS, V21

[3] Heights and isogenies of Drinfeld modules [J].

Breuer, Florian ;

Pazuki, Fabien ;

Razafinjatovo, Mahefason Heriniaina .

ACTA ARITHMETICA, 2021, 197 (02) :111-128

[4] ON THE COEFFICIENTS OF THE TRANSFORMATION POLYNOMIALS FOR THE ELLIPTIC MODULAR FUNCTION [J].

COHEN, P .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1984, 95 (MAY) :389-402

[5]

David S, 1999, MATH ANN, V315, P97, DOI 10.1007/s002080050319

[6]

Diamond F., 1995, CMS Conf. Proc., V17, P39

[7]

Dwork B., 1994, Ann. of Math. Stud., V133

[8] Theorem of the periods and minimum degrees of isogenies [J].

Gaudron, Eric ;

Remond, Gael .

COMMENTARII MATHEMATICI HELVETICI, 2014, 89 (02) :343-403

[9] Special points on fibered powers of elliptic surfaces [J].

Habegger, Philipp .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 685 :143-179

[10]

Husemoller D., 2004, GRADUATE TEXTS MATH, V111

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