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Quadratic points on modular curves
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Ozman, Ekin and Siksek, Samir (2018) Quadratic points on modular curves. Mathematics of Computation, 88 . pp. 2461-2484. doi:10.1090/mcom/3407 ISSN 0025-5718.
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Official URL: https://doi.org/10.1090/mcom/3407
Abstract
In this paper we determine the quadratic points on the modular curves X0(N), where the curve is non-hyperelliptic, the genus is 3, 4 or 5, and the Mordell–Weil group ofJ0(N)is finite. The values of Nare 34, 38, 42, 44, 45, 51, 52, 54, 55, 56, 63, 64, 72, 75, 81.As well as determining the non-cuspidal quadratic points, we give the j-invariants of the elliptic curves parametrized by those points, and determine if they have complex multiplication or are quadratic Q-curves.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Modular curves | ||||||||||||
Journal or Publication Title: | Mathematics of Computation | ||||||||||||
Publisher: | American Mathematical Society | ||||||||||||
ISSN: | 0025-5718 | ||||||||||||
Official Date: | 28 December 2018 | ||||||||||||
Dates: |
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Volume: | 88 | ||||||||||||
Page Range: | pp. 2461-2484 | ||||||||||||
DOI: | 10.1090/mcom/3407 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | “First published in Mathematics of Computation in 88, 2461-2484 published by the American Mathematical Society,” . | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | © Copyright 2018 American Mathematical Society | ||||||||||||
Date of first compliant deposit: | 10 October 2018 | ||||||||||||
Date of first compliant Open Access: | 10 April 2019 | ||||||||||||
RIOXX Funder/Project Grant: |
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