# Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6

@article{Desjardins2019GeometryOT, title={Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6}, author={Julie Desjardins and Bartosz Naskrkecki}, journal={arXiv: Number Theory}, year={2019} }

In this paper, we give an effective and efficient algorithm which on input takes non-zero integers $A$ and $B$ and on output produces the generators of the Mordell-Weil group of the elliptic curve over $\mathbb{Q}(t)$ given by an equation of the form $y^2=x^3+At^6+B$. Our method uses the correspondence between the 240 lines of a del Pezzo surface of degree 1 and the sections of minimal Shioda height on the corresponding elliptic surface over $\overline{\mathbb{Q}}$. For most rational elliptic…

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