The canonical height and elliptic surfaces (Q1813295)

The author determines a basis for the group of rational points of an elliptic surface over \(\mathbb{P}^ 1\) obtained from the diophantine equation \(A^ 4+B^ 4=C^ 4+D^ 4\). First he finds six independent sections via computer calculation. Next he estimates the lower bound of the height functions on the rational points by using the algorithm of Silverman. Then by comparing the heights he shows that there is no rational point which is not a linear combination of those six rational points.