# Properties

 Label 5501.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 5501.a

Label Equation
5501.a.5501.1 $$y^2 + (x^3 + x^2 + 1)y = -2x^3 - 3x^2 + x + 2$$

## L-function data

Analytic rank:$$2$$

Prime L-Factor
$$5501$$$$( 1 + T )( 1 + 9 T + 5501 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$$
$$3$$$$( 1 + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$$
$$5$$$$1 + 3 T + 11 T^{2} + 15 T^{3} + 25 T^{4}$$
$$7$$$$( 1 + T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$$
$$11$$$$( 1 - 3 T + 11 T^{2} )( 1 + 3 T + 11 T^{2} )$$
$$13$$$$1 + 6 T + 25 T^{2} + 78 T^{3} + 169 T^{4}$$
$$17$$$$1 + T - 14 T^{2} + 17 T^{3} + 289 T^{4}$$
$$19$$$$1 - 2 T^{2} + 361 T^{4}$$
$$23$$$$1 - 3 T + 11 T^{2} - 69 T^{3} + 529 T^{4}$$
$$29$$$$1 + 3 T + 37 T^{2} + 87 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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