# Properties

 Label 6982.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 6982.a

Label Equation
6982.a.13964.1 $$y^2 + (x^3 + 1)y = x^5 - 3x^3 + 2x$$

## L-function data

Analytic rank:$$2$$

Prime L-Factor
$$2$$$$( 1 + T )( 1 + T + 2 T^{2} )$$
$$3491$$$$( 1 + T )( 1 + 92 T + 3491 T^{2} )$$

Good L-factors:
Prime L-Factor
$$3$$$$1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$$
$$5$$$$1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4}$$
$$7$$$$( 1 + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$$
$$11$$$$1 + 3 T + 10 T^{2} + 33 T^{3} + 121 T^{4}$$
$$13$$$$1 - 2 T^{2} + 169 T^{4}$$
$$17$$$$( 1 - 4 T + 17 T^{2} )( 1 + 6 T + 17 T^{2} )$$
$$19$$$$1 + T + 3 T^{2} + 19 T^{3} + 361 T^{4}$$
$$23$$$$( 1 - 9 T + 23 T^{2} )( 1 + 8 T + 23 T^{2} )$$
$$29$$$$1 + 6 T + 50 T^{2} + 174 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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