Comptes Rendus
Articles du volume
Théorie des nombres
Rational points on a certain genus 2 curve
Xuan Tho Nguyen1
1 Hanoi University of Science and Technology
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1071-1073.

We give a correct proof to the fact that all rational points on the curve

y 2 =(x 2 +1)(x 2 +3)(x 2 +7)

are ±∞ and (±1,±8). This corrects previous works of Cohen [3] and Duquesne [4, 5].

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.471
Classification : 14G05, 14H99

Xuan Tho Nguyen 1

1 Hanoi University of Science and Technology
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2023__361_G6_1071_0,
     author = {Xuan Tho Nguyen},
     title = {Rational points on a certain genus 2 curve},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1071--1073},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.471},
     language = {en},
}
TY  - JOUR
AU  - Xuan Tho Nguyen
TI  - Rational points on a certain genus 2 curve
JO  - Comptes Rendus. Mathématique
PY  - 2023
SP  - 1071
EP  - 1073
VL  - 361
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.471
LA  - en
ID  - CRMATH_2023__361_G6_1071_0
ER  - 
%0 Journal Article
%A Xuan Tho Nguyen
%T Rational points on a certain genus 2 curve
%J Comptes Rendus. Mathématique
%D 2023
%P 1071-1073
%V 361
%I Académie des sciences, Paris
%R 10.5802/crmath.471
%G en
%F CRMATH_2023__361_G6_1071_0
Xuan Tho Nguyen. Rational points on a certain genus 2 curve. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1071-1073. doi : 10.5802/crmath.471. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.471/

[1] Wieb Bosma; John Cannon; Catherine Playoust The MAGMA algebra system. I. The user language, J. Symb. Comput., Volume 24 (1997) no. 3-4, pp. 235-265 | DOI | MR | Zbl

[2] Nils Bruin; Michael Stoll Two cover descent on hyperelliptic curves, Math. Comput., Volume 78 (2009) no. 268, pp. 2347-2370 | DOI | MR | Zbl

[3] Henri Cohen Number Theory. Volume II: Analytic and Mordern Tools, Graduate Texts in Mathematics, 240, Springer, 2007

[4] Sylvain Duquesne Calculs Effectifs des Points Entiers et Rationnels sur les Courbes, Ph. D. Thesis, Université Bordeaux I (2001)

[5] Sylvain Duquesne Points rationnels et méthode de Chabauty elliptique, J. Théor. Nombres Bordeaux, Volume 15 (2003) no. 1, pp. 99-113 | DOI | Numdam | MR | Zbl

[6] Eugene Victor Flynn; Joseph L. Wetherell Finding Rational Points on Bielliptic Genus 2 Curves, Manuscr. Math., Volume 100 (1999) no. 4, pp. 519-533 | DOI | MR | Zbl

[7] Michael Stoll Slides of the talk Rational Diophantine quintuples and diagonal genus 5 curves (https://www.mathe2.uni-bayreuth.de/stoll/talks/Manchester-2017-print.pdf)

[8] Michael Stoll Rational Diophantine quintuples and diagonal genus 5 curves, Acta Arith., Volume 190 (2019) no. 3, pp. 239-261 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique