# Properties

 Label 254208.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 254208.c

Label Equation
254208.c.762624.1 $$y^2 = 3x^5 - 5x^4 + 5x^3 + x^2 - 5x + 2$$

## L-function data

Analytic rank:$$1$$

Prime L-Factor
$$2$$$$1$$
$$3$$$$( 1 - T )( 1 + 2 T + 3 T^{2} )$$
$$331$$$$( 1 - T )( 1 - 20 T + 331 T^{2} )$$

Good L-factors:
Prime L-Factor
$$5$$$$1 - T - 5 T^{3} + 25 T^{4}$$
$$7$$$$( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$$
$$11$$$$1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4}$$
$$13$$$$( 1 - 4 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} )$$
$$17$$$$( 1 + 2 T + 17 T^{2} )( 1 + 5 T + 17 T^{2} )$$
$$19$$$$1 - 5 T + 18 T^{2} - 95 T^{3} + 361 T^{4}$$
$$23$$$$( 1 + 23 T^{2} )^{2}$$
$$29$$$$( 1 + 29 T^{2} )( 1 + 10 T + 29 T^{2} )$$
$\cdots$$\cdots$

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