We determine the twisting Sato–Tate group of the genus 3 hyperelliptic curve $y^2=x^8−14x^4+1$ and show that all possible subgroups of the twisting Sato–Tate group arise as the Sato–Tate group of an explicit twist of $y^2=x8−14x^4+1$. Furthermore, we prove the generalized Sato–Tate conjecture for the Jacobians of all Q-twists of the curve $y^2=x^8−14x^4+1$.
The twisting Sato-Tate group of the curve $y^2=x8-14x^4+1$
Lombardo, Davide;
2018-01-01
Abstract
We determine the twisting Sato–Tate group of the genus 3 hyperelliptic curve $y^2=x^8−14x^4+1$ and show that all possible subgroups of the twisting Sato–Tate group arise as the Sato–Tate group of an explicit twist of $y^2=x8−14x^4+1$. Furthermore, we prove the generalized Sato–Tate conjecture for the Jacobians of all Q-twists of the curve $y^2=x^8−14x^4+1$.File in questo prodotto:
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