Construction of rational elliptic surfaces with Mordell-Weil rank four (Q2839761)

In this paper the author gives for each rational elliptic surface with Mordell-Weil rank 4 a pencil of plane cubics yielding this surface. Moreover, he shows that the base points of this pencil yield a basis of the Mordell-Weil group. This extends work by \textit{D. Fusi} [Comment. Math. Univ. St. Pauli 55, No. 2, 195--205 (2006; Zbl 1132.14034)] and \textit{C. Salgado} [Comment. Math. Univ. St. Pauli 58, No. 2, 95--104 (2009; Zbl 1201.14027)], who considered the rank 6 and 7 cases and the rank 5 case, respectively.