Elliptic curves over the rationals with bad reduction at only one prime-Reference-Cited by-同舟云学术

Elliptic curves over the rationals with bad reduction at only one prime

Published:1990 Issue:189 Volume:54 Page:413-419
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Edixhoven Bas,de Groot Arnold,Top Jaap

Abstract

A list is given of elliptic curves over Q having additive reduction at exactly one prime. It is also proved that for primes congruent to 5 modulo 12, no such curves having potentially good reduction exist. This enables one to find in a number of cases a complete list of all elliptic curves with bad reduction at only one prime.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1990-54-189/S0025-5718-1990-0995209-4/S0025-5718-1990-0995209-4.pdf

Reference10 articles.

1. Lecture Notes in Mathematics, Vol. 476,1975

2. The rank of elliptic curves;Brumer, Armand;Duke Math. J.,1977

3. S. J. Edixhoven, Stable models of modular curves and applications, Ph.D. Thesis, Math. Inst., Univ. of Utrecht, 1989.

4. Lecture Notes in Mathematics;Gross, Benedict H.,1980

5. Rational isogenies of prime degree (with an appendix by D. Goldfeld);Mazur, B.;Invent. Math.,1978

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Solving -unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture;Memoirs of the American Mathematical Society;2023-06

2. Elliptic curves over the rationals with good reduction outside two odd primes;Journal of Number Theory;2019-09

3. Computing elliptic curves over $\mathbb {Q}$;Mathematics of Computation;2018-08-01

4. Computing Elliptic Curves over $$\mathbb{Q}$$ : Bad Reduction at One Prime;Recent Progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science;2017

5. Ramification in the division fields of an elliptic curve;Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg;2003-12