Points algébriques de petits degrés sur la courbe d’équation affine $$y^{2}=x^{5}+1$$
Tóm tắt
We give a parameterization of the algebraic points of degree
$$\le 3$$
over
$$\mathbb {Q}$$
on the curve
$$ y^{2}=x^{5}+1. $$
This result extends a previous result of Schaefer who described in Schaefer (Math Ann 310:447–471, 1998) the set of algebraic points of degree
$$\le 2 $$
over
$$\mathbb {Q}$$
.
Tài liệu tham khảo
Schaefer, E.F.: Computing a Selmer group of a Jacobian using functions on the curve. Math. Ann. 310, 447–471 (1998)
Griffiths, P. A.: Introduction to algebraic curves. In: Translations of mathematical monographs, vol. 76. American Mathematical Society, Providence, RI (1989)