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arXiv · 2006.14966

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

Abbey Bourdon·David R. Gill·Jeremy Rouse·Lori D. Watson
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Abstract

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 $N$.

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Abbey Bourdon, David R. Gill, Jeremy Rouse, Lori D. Watson. 2020-06-26. Odd degree isolated points on $X_1(N)$ with rational $j$-invariant. https://arxiv.org/abs/2006.14966

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