# Properties

 Label 100352.c Sato-Tate group $\mathrm{USp}(4)$ $$\End(J_{\overline{\Q}}) \otimes \R$$ $$\R$$ $$\End(J_{\overline{\Q}}) \otimes \Q$$ $$\Q$$ $$\overline{\Q}$$-simple yes $$\mathrm{GL}_2$$-type no

# Related objects

## Genus 2 curves in isogeny class 100352.c

Label Equation
100352.c.100352.1 $$y^2 = x^5 - 9x^3 + 7x^2 + 14x - 14$$

## L-function data

Analytic rank:$$1$$

Prime L-Factor
$$2$$$$1$$
$$7$$$$1 + 7 T^{2}$$

Good L-factors:
Prime L-Factor
$$3$$$$( 1 - 2 T + 3 T^{2} )( 1 + T + 3 T^{2} )$$
$$5$$$$( 1 - 2 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$$
$$11$$$$( 1 - T + 11 T^{2} )( 1 + 2 T + 11 T^{2} )$$
$$13$$$$1 + 6 T^{2} + 169 T^{4}$$
$$17$$$$( 1 - T + 17 T^{2} )( 1 + 2 T + 17 T^{2} )$$
$$19$$$$1 + T - 16 T^{2} + 19 T^{3} + 361 T^{4}$$
$$23$$$$1 + T + 6 T^{2} + 23 T^{3} + 529 T^{4}$$
$$29$$$$( 1 - 2 T + 29 T^{2} )( 1 + 6 T + 29 T^{2} )$$
$\cdots$$\cdots$

$$\mathrm{ST} =$$ $\mathrm{USp}(4)$
Not of $$\GL_2$$-type over $$\Q$$
All $$\overline{\Q}$$-endomorphisms of the Jacobian are defined over $$\Q$$.