Linda Frey

Let $E$ be an elliptic curve defined over $\mathbb{Q}$. We will show that there exists an explicit constant $C$ which is only dependent on the conductor and the $j-$invariant of $E$ such that the absolute logarithmic Weil height of an $\alpha \in \mathbb{Q} (E_{tor})^* - \mu_\infty $

is always greater than $C$ where $E_\text{tor}$ denotes all the torsion points of $E$ and $\mu_\infty$ are the roots of unity.