Counting odd genus $2$ curves with a marked rational $3$-torsion point

Elvira Lupoian; Lazar Radicevic

Counting odd genus $2$ curves with a marked rational $3$-torsion point

Number Theory 2026-07-10 v1

Authors: Elvira Lupoian , Lazar Radicevic

Abstract

In this paper we count, ordered by naive height, the genus $2$ curves over the rationals which admit a monic Weierstrass model of odd degree and whose Jacobian has a marked rational $3$ -torsion point.

Keywords

genus 2 curves naive height Jacobian 3-torsion point Weierstrass model arithmetic statistics

Cite

@article{arxiv.2607.09483,
  title  = {Counting odd genus $2$ curves with a marked rational $3$-torsion point},
  author = {Elvira Lupoian and Lazar Radicevic},
  journal= {arXiv preprint arXiv:2607.09483},
  year   = {2026}
}

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