Let $\mathcal N$ be the moduli space of sextics with 3 (3,4)-cusps. The quotient moduli space ${\mathcal N}/G$ is one-dimensional and consists of two components, ${\mathcal N}_{torus}/G$ and ${\mathcal N}_{gen}/G$. By quadratic transformations, they are transformed into one-parameter families $C_s$ and $D_s$ of cubic curves respectively. We study the Mordell-Weil torsion groups of cubic curves $C_s$ over $\bfQ$ and $D_s$ over $\bfQ(\sqrt{-3})$ respectively. We show that $C_{s}$ has the torsion...

Source: http://arxiv.org/abs/math/9912041v3