Annales Mathématiques Africaines

Points algébriques de degré au plus 4 sur la courbe
d’équation affine y² = x(x - 3)(x - 4)(x - 6)(x - 7)

Boubacar Sidy BALDE ⁽¹⁾ and Oumar SALL ⁽²⁾
Laboratoire: Mathématiques et Applications (LMA),
U.F.R des Sciences et Technologies,
Université Assane Seck de Ziguinchor,
BP 523 Ziguinchor Sénégal

Mathematics Subject Classification: (2010) 14H50, 14H40, 11D68
Key words: Mordell-Weil Group. Jacobian. Galois Conjugates. Algebraic extensions. The Abel-Jacobi theorem. Linear systems.

Abstract:

In this work, we use the finiteness of the Mordell-weil group of the Jacobian variety of and the Riemann Roch spaces to determine the set of algebraic points of degree at most four over ℚ on the affine curve : y² = x(x - 3)(x - 4)(x - 6)(x - 7).
The results obtained extend the work of Daniel M.Gordon and David Grant in [1], who determined the Mordell-Weil group J(ℚ) and the set of rational points on the same curve.