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arXiv · 1608.06784

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

Sonny Arora·Victoria Cantoral-Farfán·Aaron Landesman·Davide Lombardo·Jackson S. Morrow
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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 $y^2 = x^{8} - 14x^4 + 1$. Furthermore, we prove the generalized Sato-Tate conjecture for the Jacobians of all $\mathbb Q$-twists of the curve $y^2 = x^{8} - 14x^4 + 1$.

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Sonny Arora, Victoria Cantoral-Farfán, Aaron Landesman, Davide Lombardo, Jackson S. Morrow. 2016-08-24. The twisting Sato-Tate group of the curve $y^2 = x^{8} - 14x^4 + 1$. https://arxiv.org/abs/1608.06784

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