Higher descents on an elliptic curve with a rational 2-torsion point
Higher descents on an elliptic curve with a rational 2-torsion point
Let $E$ be an elliptic curve over a number field $K$. Descent calculations on $E$ can be used to find upper bounds for the rank of the Mordell-Weil group, and to compute covering curves that assist in the search for generators of this group. The general method of $4$-descent, developed …