# Properties

 Label 6201.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 6201.a

Label Equation
6201.a.241839.1 $$y^2 + (x^3 + 1)y = 2x^5 - 13x^3 + 21x^2 - 12x + 2$$

## L-function data

Analytic rank:$$2$$

Prime L-Factor
$$3$$$$1 + 3 T + 3 T^{2}$$
$$13$$$$( 1 - T )( 1 + 5 T + 13 T^{2} )$$
$$53$$$$( 1 - T )( 1 + 10 T + 53 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$$
$$5$$$$( 1 + 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$
$$7$$$$1 + 4 T + 16 T^{2} + 28 T^{3} + 49 T^{4}$$
$$11$$$$1 + 14 T^{2} + 121 T^{4}$$
$$17$$$$1 + T - 10 T^{2} + 17 T^{3} + 289 T^{4}$$
$$19$$$$( 1 - 7 T + 19 T^{2} )( 1 + 6 T + 19 T^{2} )$$
$$23$$$$1 + 9 T + 42 T^{2} + 207 T^{3} + 529 T^{4}$$
$$29$$$$1 + 3 T - 6 T^{2} + 87 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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