# Properties

 Label 7211.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 7211.a

Label Equation
7211.a.7211.1 $$y^2 + (x^3 + 1)y = -x^4 + 2x^3 - 2x^2$$

## L-function data

Analytic rank:$$2$$

Prime L-Factor
$$7211$$$$( 1 + T )( 1 + 70 T + 7211 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$$
$$3$$$$1 + 3 T + 5 T^{2} + 9 T^{3} + 9 T^{4}$$
$$5$$$$( 1 + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$
$$7$$$$( 1 + 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$$
$$11$$$$1 - T + 7 T^{2} - 11 T^{3} + 121 T^{4}$$
$$13$$$$1 + 3 T + 7 T^{2} + 39 T^{3} + 169 T^{4}$$
$$17$$$$( 1 - 3 T + 17 T^{2} )( 1 + 4 T + 17 T^{2} )$$
$$19$$$$1 + T + 11 T^{2} + 19 T^{3} + 361 T^{4}$$
$$23$$$$( 1 - 2 T + 23 T^{2} )( 1 + 6 T + 23 T^{2} )$$
$$29$$$$1 - 2 T + 38 T^{2} - 58 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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