Properties

 Label 100325.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 100325.b

Label Equation
100325.b.100325.1 $$y^2 + (x^2 + x + 1)y = -x^5 + 3x^4 - 10x^2 + 2x + 8$$

L-function data

Analytic rank:$$1$$

Prime L-Factor
$$5$$$$( 1 - T )( 1 + T )$$
$$4013$$$$( 1 + T )( 1 + 83 T + 4013 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$$
$$3$$$$1 + 9 T^{4}$$
$$7$$$$1 - 3 T + 7 T^{2} - 21 T^{3} + 49 T^{4}$$
$$11$$$$1 + 10 T^{2} + 121 T^{4}$$
$$13$$$$1 + T + 15 T^{2} + 13 T^{3} + 169 T^{4}$$
$$17$$$$1 + 8 T + 42 T^{2} + 136 T^{3} + 289 T^{4}$$
$$19$$$$1 + 7 T + 34 T^{2} + 133 T^{3} + 361 T^{4}$$
$$23$$$$1 + 18 T^{2} + 529 T^{4}$$
$$29$$$$1 - 6 T + 32 T^{2} - 174 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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