# Properties

 Label 20532.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 20532.b

Label Equation
20532.b.123192.1 $$y^2 + (x^3 + x + 1)y = 2x^6 - 3x^4 - x$$

## L-function data

Analytic rank:$$2$$

Prime L-Factor
$$2$$$$1 + T + T^{2}$$
$$3$$$$( 1 + T )( 1 + 2 T + 3 T^{2} )$$
$$29$$$$( 1 + T )( 1 - T + 29 T^{2} )$$
$$59$$$$( 1 + T )( 1 + 4 T + 59 T^{2} )$$

Good L-factors:
Prime L-Factor
$$5$$$$1 + 4 T + 9 T^{2} + 20 T^{3} + 25 T^{4}$$
$$7$$$$1 + 2 T + 5 T^{2} + 14 T^{3} + 49 T^{4}$$
$$11$$$$1 + 7 T + 31 T^{2} + 77 T^{3} + 121 T^{4}$$
$$13$$$$1 + 3 T + 7 T^{2} + 39 T^{3} + 169 T^{4}$$
$$17$$$$1 + 6 T + 21 T^{2} + 102 T^{3} + 289 T^{4}$$
$$19$$$$( 1 - 7 T + 19 T^{2} )( 1 + 5 T + 19 T^{2} )$$
$$23$$$$1 + 4 T + 2 T^{2} + 92 T^{3} + 529 T^{4}$$
$\cdots$$\cdots$

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