Properties

 Label 704.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 704.a

Label Equation
704.a.45056.1 $$y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$$

L-function data

Analytic rank:$$0$$

Prime L-Factor
$$2$$$$1 + 2 T^{2}$$
$$11$$$$( 1 - T )( 1 + 11 T^{2} )$$

Good L-factors:
Prime L-Factor
$$3$$$$1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4}$$
$$5$$$$( 1 - 2 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$$
$$7$$$$( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$$
$$13$$$$( 1 - 2 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$
$$17$$$$( 1 - 6 T + 17 T^{2} )( 1 + 6 T + 17 T^{2} )$$
$$19$$$$1 - 2 T^{2} + 361 T^{4}$$
$$23$$$$1 - 3 T - 2 T^{2} - 69 T^{3} + 529 T^{4}$$
$$29$$$$( 1 - 8 T + 29 T^{2} )( 1 + 6 T + 29 T^{2} )$$
$\cdots$$\cdots$

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