TITLE:
Algebraic Points of Any Degree l with (l ≥ 9) over Q on the Affine Equation Curve C3 (11): y11 = x3(x-1)3
AUTHORS:
Boubacar Sidy Balde, Mohamadou Mor Diogou Diallo, Oumar Sall
KEYWORDS:
Mordell-Weil Group, Jacobian, Galois Conjugates, Algebraic Extensions, the Abel-Jacobi Theorem, Linear Systems
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.9,
September
16,
2022
ABSTRACT: In this work, we use the finiteness of the Mordell-weil group and the Riemann Roch spaces to give a geometric parametrization of the set of algebraic points of any given degree over the field of rational numbers Q on curve C3 (11): y11 = x3 (x-1)3. This result is a special case of quotients of Fermat curves Cr,s (p) : yp = xr(x-1)s, 1 ≤ r, s, r + s ≤ p-1 for p = 11 and r = s = 3. The results obtained extend the work of Gross and Rohrlich who determined the set of algebraic points on C1(11)(K)of degree at most 2 on Q.