The distribution of the Tamagawa ratio in the family of elliptic curves with a two-torsion point

Zev Klagsbrun, Robert J. Lemke Oliver

In recent work, Bhargava and Shankar have shown that the average size of the $2$-Selmer group of an elliptic curve over $\mathbb{Q}$ is exactly $3$, and Bhargava and Ho have shown…