# Properties

 Label 1532.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 1532.a

Label Equation
1532.a.1532.1 $$y^2 + (x^3 + 1)y = -x - 1$$
1532.a.392192.1 $$y^2 + (x^2 + x + 1)y = x^5 + 7x^4 - 53x^2 + 12x - 1$$

## L-function data

Analytic rank:$$0$$

Prime L-Factor
$$2$$$$1 + T^{2}$$
$$383$$$$( 1 + T )( 1 - 24 T + 383 T^{2} )$$

Good L-factors:
Prime L-Factor
$$3$$$$1 + 9 T^{4}$$
$$5$$$$( 1 - T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$
$$7$$$$1 - T - 2 T^{2} - 7 T^{3} + 49 T^{4}$$
$$11$$$$1 + 3 T + 17 T^{2} + 33 T^{3} + 121 T^{4}$$
$$13$$$$( 1 + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$
$$17$$$$1 - 3 T - T^{2} - 51 T^{3} + 289 T^{4}$$
$$19$$$$1 - 2 T + 18 T^{2} - 38 T^{3} + 361 T^{4}$$
$$23$$$$1 - 6 T + 24 T^{2} - 138 T^{3} + 529 T^{4}$$
$$29$$$$1 - 4 T + 38 T^{2} - 116 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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