# Properties

 Label 1077.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 1077.b

Label Equation
1077.b.1077.1 $$y^2 + x^3y = x^5 + x^4 - x - 2$$
1077.b.1077.2 $$y^2 + y = x^5 + 14x^4 + 38x^3 - 79x^2 + 15x - 1$$

## L-function data

Analytic rank:$$0$$

Prime L-Factor
$$3$$$$( 1 + T )( 1 + T + 3 T^{2} )$$
$$359$$$$( 1 + T )( 1 - 30 T + 359 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$$
$$5$$$$1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4}$$
$$7$$$$1 + 3 T + 6 T^{2} + 21 T^{3} + 49 T^{4}$$
$$11$$$$( 1 - 2 T + 11 T^{2} )( 1 + 3 T + 11 T^{2} )$$
$$13$$$$( 1 - 7 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$
$$17$$$$1 - 2 T + 6 T^{2} - 34 T^{3} + 289 T^{4}$$
$$19$$$$( 1 - 4 T + 19 T^{2} )( 1 + 5 T + 19 T^{2} )$$
$$23$$$$1 - 4 T + 36 T^{2} - 92 T^{3} + 529 T^{4}$$
$$29$$$$( 1 - 6 T + 29 T^{2} )( 1 + 29 T^{2} )$$
$\cdots$$\cdots$

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