Davide Lombardo

The twisting Sato–Tate group of the curve \(y^2 = x^{8} - 14x^4 + 1\)

We determine the twisting Sato–Tate group of the genus 3 hyperelliptic curve

Computing twists of hyperelliptic curves

y^2 = x^{8} - 14x^4 + 1

BOUNDS FOR SERRE'S OPEN IMAGE THEOREM FOR ELLIPTIC CURVES OVER NUMBER FIELDS

y2=x8-14x4+1 and show that all possible subgroups of the twisting Sato–Tate group arise as the Sato–Tate group of an explicit twist of

\ell

y^2 = x^{8} - 14x^4 + 1

Explicit open image theorems for abelian varieties with trivial endomorphism ring

y2=x8-14x4+1. Furthermore, we prove the generalized Sato–Tate conjecture for the Jacobians of all