# Properties

 Label 100130.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 100130.a

Label Equation
100130.a.200260.1 $$y^2 + (x^2 + x + 1)y = x^6 + 5x^5 + 6x^4 + x^2 + x$$

## L-function data

Analytic rank:$$2$$

Prime L-Factor
$$2$$$$( 1 + T )( 1 + T + 2 T^{2} )$$
$$5$$$$( 1 + T )( 1 + 5 T^{2} )$$
$$17$$$$( 1 + T )( 1 + 6 T + 17 T^{2} )$$
$$19$$$$( 1 - T )( 1 + 6 T + 19 T^{2} )$$
$$31$$$$( 1 - T )( 1 + 6 T + 31 T^{2} )$$

Good L-factors:
Prime L-Factor
$$3$$$$( 1 - T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$$
$$7$$$$( 1 + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$$
$$11$$$$1 - 2 T + 12 T^{2} - 22 T^{3} + 121 T^{4}$$
$$13$$$$1 + T + 8 T^{2} + 13 T^{3} + 169 T^{4}$$
$$23$$$$1 - 2 T - 6 T^{2} - 46 T^{3} + 529 T^{4}$$
$$29$$$$1 + 34 T^{2} + 841 T^{4}$$
$\cdots$$\cdots$

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