Elliptic curves over the rationals with good reduction outside two odd primes

We classify elliptic curves over Q with a rational point of order 2 or ≥4 and good reduction outside two odd primes. We also exhibit some families of elliptic curves with a rational point of order 3, collect some general existence/non-existence results, and present some information concerning upper...

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Bibliographic Details
Published inJournal of number theory Vol. 202; pp. 254 - 277
Main Authors Dąbrowski, Andrzej, Jędrzejak, Tomasz
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2019
Subjects
Class number
Diophantine equation
Elliptic curve
Rational point
14G05
Class number
Rational point
Diophantine equation
14H52
Elliptic curve
14G25
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ISSN0022-314X
1096-1658
DOI10.1016/j.jnt.2019.01.007

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Summary:We classify elliptic curves over Q with a rational point of order 2 or ≥4 and good reduction outside two odd primes. We also exhibit some families of elliptic curves with a rational point of order 3, collect some general existence/non-existence results, and present some information concerning upper bounds for the rank.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2019.01.007