# Properties

 Label 1164.b 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 1164.b

Label Equation
1164.b.670464.1 $$y^2 + (x^2 + x + 1)y = 2x^5 - 2x^4 + x^3 - x^2$$

## L-function data

Analytic rank:$$0$$

Prime L-Factor
$$2$$$$( 1 - T )( 1 + T )$$
$$3$$$$( 1 - T )( 1 + 3 T + 3 T^{2} )$$
$$97$$$$( 1 + T )( 1 + 7 T + 97 T^{2} )$$

Good L-factors:
Prime L-Factor
$$5$$$$1 - T + T^{2} - 5 T^{3} + 25 T^{4}$$
$$7$$$$1 + 5 T + 15 T^{2} + 35 T^{3} + 49 T^{4}$$
$$11$$$$1 - T - 5 T^{2} - 11 T^{3} + 121 T^{4}$$
$$13$$$$( 1 - 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$
$$17$$$$1 + 3 T + 13 T^{2} + 51 T^{3} + 289 T^{4}$$
$$19$$$$1 + T - 25 T^{2} + 19 T^{3} + 361 T^{4}$$
$$23$$$$1 - 8 T + 40 T^{2} - 184 T^{3} + 529 T^{4}$$
$$29$$$$( 1 - 9 T + 29 T^{2} )( 1 + 6 T + 29 T^{2} )$$
$\cdots$$\cdots$

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