# Properties

 Label 100124.a 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 100124.a

Label Equation
100124.a.400496.1 $$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^2 - 2x$$

## L-function data

Analytic rank:$$1$$

Prime L-Factor
$$2$$$$( 1 - T )( 1 + T )$$
$$25031$$$$( 1 + T )( 1 - 56 T + 25031 T^{2} )$$

Good L-factors:
Prime L-Factor
$$3$$$$1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4}$$
$$5$$$$1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4}$$
$$7$$$$1 - 3 T + 6 T^{2} - 21 T^{3} + 49 T^{4}$$
$$11$$$$( 1 - 4 T + 11 T^{2} )( 1 + 5 T + 11 T^{2} )$$
$$13$$$$1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4}$$
$$17$$$$( 1 - 4 T + 17 T^{2} )( 1 + 6 T + 17 T^{2} )$$
$$19$$$$( 1 - 4 T + 19 T^{2} )( 1 + 5 T + 19 T^{2} )$$
$$23$$$$1 - T + 14 T^{2} - 23 T^{3} + 529 T^{4}$$
$$29$$$$( 1 - 2 T + 29 T^{2} )( 1 + 6 T + 29 T^{2} )$$
$\cdots$$\cdots$

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