Properties

 Label 100128.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 100128.a

Label Equation
100128.a.801024.1 $$y^2 + (x^2 + 1)y = 4x^5 - x^4 - 13x^3 - 2x^2 + 7x - 2$$

L-function data

Analytic rank:$$0$$

Prime L-Factor
$$2$$$$1 + T$$
$$3$$$$( 1 - T )( 1 + T + 3 T^{2} )$$
$$7$$$$( 1 - T )( 1 - 2 T + 7 T^{2} )$$
$$149$$$$( 1 - T )( 1 + 4 T + 149 T^{2} )$$

Good L-factors:
Prime L-Factor
$$5$$$$1 - T + 7 T^{2} - 5 T^{3} + 25 T^{4}$$
$$11$$$$1 - T - 6 T^{2} - 11 T^{3} + 121 T^{4}$$
$$13$$$$1 - 3 T + 5 T^{2} - 39 T^{3} + 169 T^{4}$$
$$17$$$$1 - 7 T + 41 T^{2} - 119 T^{3} + 289 T^{4}$$
$$19$$$$1 + 3 T + 26 T^{2} + 57 T^{3} + 361 T^{4}$$
$$23$$$$1 - 3 T - 13 T^{2} - 69 T^{3} + 529 T^{4}$$
$$29$$$$1 + 4 T + 48 T^{2} + 116 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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