# Properties

 Label 100096.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 100096.c

Label Equation
100096.c.100096.1 $$y^2 = x^5 - 9x^3 - 5x^2 + 21x + 20$$

## L-function data

Analytic rank:$$0$$

Prime L-Factor
$$2$$$$1$$
$$17$$$$( 1 - T )( 1 + 4 T + 17 T^{2} )$$
$$23$$$$( 1 + T )( 1 - 2 T + 23 T^{2} )$$

Good L-factors:
Prime L-Factor
$$3$$$$( 1 - 3 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$$
$$5$$$$( 1 - 2 T + 5 T^{2} )^{2}$$
$$7$$$$1 - 2 T - 2 T^{2} - 14 T^{3} + 49 T^{4}$$
$$11$$$$1 - 6 T^{2} + 121 T^{4}$$
$$13$$$$1 - 5 T + 16 T^{2} - 65 T^{3} + 169 T^{4}$$
$$19$$$$( 1 + 19 T^{2} )( 1 + 6 T + 19 T^{2} )$$
$$29$$$$1 + T + 12 T^{2} + 29 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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