# Properties

 Label 100152.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 100152.a

Label Equation
100152.a.600912.1 $$y^2 + y = x^6 - 2x^5 - 6x^4 - 4x^3 + x$$

## L-function data

Analytic rank:$$2$$

Prime L-Factor
$$2$$$$1 + 2 T + 2 T^{2}$$
$$3$$$$( 1 - T )( 1 + T )$$
$$13$$$$( 1 - T )( 1 + 5 T + 13 T^{2} )$$
$$107$$$$( 1 - T )( 1 + 12 T + 107 T^{2} )$$

Good L-factors:
Prime L-Factor
$$5$$$$( 1 + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$
$$7$$$$1 + 4 T + 13 T^{2} + 28 T^{3} + 49 T^{4}$$
$$11$$$$1 + 3 T + 16 T^{2} + 33 T^{3} + 121 T^{4}$$
$$17$$$$1 - 8 T^{2} + 289 T^{4}$$
$$19$$$$1 + 2 T + 4 T^{2} + 38 T^{3} + 361 T^{4}$$
$$23$$$$1 + 2 T + 7 T^{2} + 46 T^{3} + 529 T^{4}$$
$$29$$$$1 - 4 T + 23 T^{2} - 116 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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