# Properties

 Label 925.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 925.a

Label Equation
925.a.925.1 $$y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$$
925.a.23125.1 $$y^2 + xy = 5x^5 + x^4 - 19x^3 + 18x^2 - 5x$$

## L-function data

Analytic rank:$$0$$

Prime L-Factor
$$5$$$$( 1 - T )( 1 + T )$$
$$37$$$$( 1 - T )( 1 - 6 T + 37 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$1 + T + 2 T^{3} + 4 T^{4}$$
$$3$$$$1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4}$$
$$7$$$$1 - T + 6 T^{2} - 7 T^{3} + 49 T^{4}$$
$$11$$$$1 + T - 6 T^{2} + 11 T^{3} + 121 T^{4}$$
$$13$$$$1 + 2 T - 6 T^{2} + 26 T^{3} + 169 T^{4}$$
$$17$$$$1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4}$$
$$19$$$$( 1 - 4 T + 19 T^{2} )( 1 + 4 T + 19 T^{2} )$$
$$23$$$$( 1 - 4 T + 23 T^{2} )( 1 + 8 T + 23 T^{2} )$$
$$29$$$$1 - 2 T - 14 T^{2} - 58 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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