# Properties

 Label 1184.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 1184.a

Label Equation
1184.a.2368.1 $$y^2 + y = 2x^5 + x^4 + x^2 + x$$
1184.a.606208.2 $$y^2 = x^6 - 2x^5 + 5x^4 - 4x^3 + 6x^2 - 2x + 2$$
1184.a.606208.1 $$y^2 = 2x^5 + x^4 - 8x^3 - 8x^2 - 2x$$

## L-function data

Analytic rank:$$0$$

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

Good L-factors:
Prime L-Factor
$$3$$$$1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4}$$
$$5$$$$( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$
$$7$$$$1 + 3 T + 6 T^{2} + 21 T^{3} + 49 T^{4}$$
$$11$$$$( 1 - 5 T + 11 T^{2} )( 1 + 4 T + 11 T^{2} )$$
$$13$$$$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$
$$17$$$$1 + 2 T - 6 T^{2} + 34 T^{3} + 289 T^{4}$$
$$19$$$$( 1 - 4 T + 19 T^{2} )( 1 + 4 T + 19 T^{2} )$$
$$23$$$$( 1 - 8 T + 23 T^{2} )( 1 + 2 T + 23 T^{2} )$$
$$29$$$$( 1 - 6 T + 29 T^{2} )( 1 + 2 T + 29 T^{2} )$$
$\cdots$$\cdots$

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