The twisting Sato-Tate group of the curve $y^2 = x^8 - 14x^2 + 1$
Published in Mathematische Zeitschrift, 2018
Recommended citation: The twisting Sato-Tate group of the curve $y^2 = x^8 − 14x^22 + 1$, with Victoria Cantoral-Farfán, Aaron Landesman, Davide Lombardo, Jackson S. Morrow. Mathematische Zeitschrift (2018): 1-32. https://link.springer.com/article/10.1007/s00209-018-2049-6
We determine the twisting Sato–Tate group of the genus 3 hyperelliptic curve $y^2 = x^8 - 14x^2 + 1$ and show that all possible subgroups of the twisting Sato–Tate group arise as the Sato–Tate group of an explicit twist of $y^2 = x^8 - 14x^2 + 1$ . Furthermore, we prove the generalized Sato–Tate conjecture for the Jacobians of all $\mathbb{Q}$-twists of the curve $y^2 = x^8 - 14x^2 + 1$
Recommended citation: ‘The twisting Sato-Tate group of the curve $y^2 = x^8 − 14x^22 + 1$, with Victoria Cantoral-Farfán, Aaron Landesman, Davide Lombardo, Jackson S. Morrow. Mathematische Zeitschrift (2018): 1-32.’