# Properties

 Label 100224.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 100224.b

Label Equation
100224.b.601344.1 $$y^2 = x^5 + x^4 - 2x^3 + 4x^2 - 2x + 1$$

## L-function data

Analytic rank:$$1$$

Prime L-Factor
$$2$$$$1$$
$$3$$$$1 + T$$
$$29$$$$( 1 + T )( 1 + 4 T + 29 T^{2} )$$

Good L-factors:
Prime L-Factor
$$5$$$$( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$
$$7$$$$( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$$
$$11$$$$( 1 + 11 T^{2} )( 1 + 5 T + 11 T^{2} )$$
$$13$$$$1 - 3 T + 12 T^{2} - 39 T^{3} + 169 T^{4}$$
$$17$$$$1 - 3 T - 2 T^{2} - 51 T^{3} + 289 T^{4}$$
$$19$$$$( 1 - 2 T + 19 T^{2} )( 1 + 4 T + 19 T^{2} )$$
$$23$$$$( 1 + 23 T^{2} )( 1 + 4 T + 23 T^{2} )$$
$\cdots$$\cdots$

## Sato-Tate group

$$\mathrm{ST} =$$ $\mathrm{USp}(4)$

## Endomorphisms of the Jacobian

Not of $$\GL_2$$-type over $$\Q$$

All $$\overline{\Q}$$-endomorphisms of the Jacobian are defined over $$\Q$$.

More complete information on endomorphism algebras and rings can be found on the pages of the individual curves in the isogeny class.