Effective Mordell for curves with enough automorphisms

Natalia Garcia-Fritz; Hector Pasten

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arXiv · 2503.10443

Effective Mordell for curves with enough automorphisms

Natalia Garcia-Fritz·Hector Pasten

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Abstract

We prove a completely explicit and effective upper bound for the N\'eron--Tate height of rational points of curves of genus at least $2$ over number fields, provided that they have enough automorphisms with respect to the Mordell--Weil rank of their jacobian. Our arguments build on Arakelov theory for arithmetic surfaces. Our bounds are practical, and we illustrate this by explicitly computing the rational points of a certain genus $2$ curve whose jacobian has Mordell--Weil rank $2$.

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Natalia Garcia-Fritz, Hector Pasten. 2025-03-13. Effective Mordell for curves with enough automorphisms. https://arxiv.org/abs/2503.10443

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