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POINTS OF LOW DEGREES ON THE TSUZUKI-YAMAUCHI SMOOTH CURVE
Keywords:
degree of algebraic point, curve, linear system, Mordell-Weil group, JacobianDOI:
https://doi.org/10.17654/0972415X24004Abstract
We give the set of algebraic points of degree at most 3 over $\mathbb{Q}$ on the affine curve $C: y^2=5\left(1-x^5\right)$ studied by Tsuzuki and Yamauchi in [3].
Received: February 1, 2024
Revised: February 12, 2024
Accepted: March 29, 2024
References
P. A. Griffiths, Introduction to algebraic curves, Translations of Mathematical Monographs, American Mathematical Society, Providence, Volume 76, 1989.
El Hadji SOW, Moussa FALL and Oumar SALL, Algebraic points on the genus 2 curve Journal of Contemporary Applied Mathematics 14(1) (2024), 28-32.
N. Tsuzuki and T. Yamauchi, Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials, arXiv:2008.09852v4 [math.NT] 28 Sep 2022.
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