Properties

 Label 353.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 353.a

Label Equation
353.a.353.1 $$y^2 + (x^3 + x + 1)y = x^2$$

L-function data

Analytic rank:$$0$$

Prime L-Factor
$$353$$$$( 1 + T )( 1 + 9 T + 353 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$$
$$3$$$$1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$$
$$5$$$$1 - T + 2 T^{2} - 5 T^{3} + 25 T^{4}$$
$$7$$$$1 - 6 T^{2} + 49 T^{4}$$
$$11$$$$1 - 2 T + T^{2} - 22 T^{3} + 121 T^{4}$$
$$13$$$$1 + T - 8 T^{2} + 13 T^{3} + 169 T^{4}$$
$$17$$$$( 1 - 7 T + 17 T^{2} )( 1 + T + 17 T^{2} )$$
$$19$$$$1 + 6 T + 35 T^{2} + 114 T^{3} + 361 T^{4}$$
$$23$$$$1 + 2 T + 27 T^{2} + 46 T^{3} + 529 T^{4}$$
$$29$$$$( 1 - 8 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} )$$
$\cdots$$\cdots$

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