Odd degree isolated points on $X_1(N)$ with rational $j$-invariant

Let $C$ be a curve defined over a number field $k$. We say a closed point $x\in C$ of degree $d$ is isolated if it does not belong to an infinite family of degree $d$ points parametrized by the projective line or a positive rank abelian subvariety of the curve's Jacobian. Building on work of Bo...

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Main Authors: Bourdon, Abbey, Gill, David R., Rouse, Jeremy, Watson, Lori D.
Format: Article in Journal/Newspaper
Language:unknown
Published: arXiv 2020
Subjects:
Number Theory math.NT
FOS Mathematics
14G35, 11G05
ejder
Online Access:https://dx.doi.org/10.48550/arxiv.2006.14966
https://arxiv.org/abs/2006.14966
id ftdatacite:10.48550/arxiv.2006.14966
record_format openpolar
spelling ftdatacite:10.48550/arxiv.2006.14966 2023-05-15T16:04:54+02:00 Odd degree isolated points on $X_1(N)$ with rational $j$-invariant Bourdon, Abbey Gill, David R. Rouse, Jeremy Watson, Lori D. 2020 https://dx.doi.org/10.48550/arxiv.2006.14966 https://arxiv.org/abs/2006.14966 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Number Theory math.NT FOS Mathematics 14G35, 11G05 Article CreativeWork article Preprint 2020 ftdatacite https://doi.org/10.48550/arxiv.2006.14966 2022-03-10T15:32:16Z Let $C$ be a curve defined over a number field $k$. We say a closed point $x\in C$ of degree $d$ is isolated if it does not belong to an infinite family of degree $d$ points parametrized by the projective line or a positive rank abelian subvariety of the curve's Jacobian. Building on work of Bourdon, Ejder, Liu, Odumodu, and Viray, we characterize elliptic curves with rational $j$-invariant which give rise to an isolated point of odd degree on $X_1(N)/\mathbb{Q}$ for some positive integer $N$. : 26 pages Article in Journal/Newspaper ejder DataCite Metadata Store (German National Library of Science and Technology)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Number Theory math.NT
FOS Mathematics
14G35, 11G05
spellingShingle Number Theory math.NT
FOS Mathematics
14G35, 11G05
Bourdon, Abbey
Gill, David R.
Rouse, Jeremy
Watson, Lori D.
Odd degree isolated points on $X_1(N)$ with rational $j$-invariant
topic_facet Number Theory math.NT
FOS Mathematics
14G35, 11G05
description Let $C$ be a curve defined over a number field $k$. We say a closed point $x\in C$ of degree $d$ is isolated if it does not belong to an infinite family of degree $d$ points parametrized by the projective line or a positive rank abelian subvariety of the curve's Jacobian. Building on work of Bourdon, Ejder, Liu, Odumodu, and Viray, we characterize elliptic curves with rational $j$-invariant which give rise to an isolated point of odd degree on $X_1(N)/\mathbb{Q}$ for some positive integer $N$. : 26 pages
format Article in Journal/Newspaper
author Bourdon, Abbey
Gill, David R.
Rouse, Jeremy
Watson, Lori D.
author_facet Bourdon, Abbey
Gill, David R.
Rouse, Jeremy
Watson, Lori D.
author_sort Bourdon, Abbey
title Odd degree isolated points on $X_1(N)$ with rational $j$-invariant
title_short Odd degree isolated points on $X_1(N)$ with rational $j$-invariant
title_full Odd degree isolated points on $X_1(N)$ with rational $j$-invariant
title_fullStr Odd degree isolated points on $X_1(N)$ with rational $j$-invariant
title_full_unstemmed Odd degree isolated points on $X_1(N)$ with rational $j$-invariant
title_sort odd degree isolated points on $x_1(n)$ with rational $j$-invariant
publisher arXiv
publishDate 2020
url https://dx.doi.org/10.48550/arxiv.2006.14966
https://arxiv.org/abs/2006.14966
genre ejder
genre_facet ejder
op_rights arXiv.org perpetual, non-exclusive license
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
op_doi https://doi.org/10.48550/arxiv.2006.14966
_version_ 1766400542508056576

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