Nondegeneracy and Sato-Tate Distributions of Two Families of Jacobian Varieties

Melissa Emory, Heidi Goodson

We consider the curves $y^2=x^{2^m}-1$ and $y^2=x^{2^d+1}-x$ over the rationals. These curves are related via their associated Jacobian varieties in that the Jacobians of the la…