# Properties

 Label 1062.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

# Learn more about

## Genus 2 curves in isogeny class 1062.a

Label Equation
1062.a.6372.1 $$y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x$$

## L-function data

Analytic rank:$$1$$

Bad L-factors:
Prime L-Factor
$$2$$$$( 1 + T )( 1 + T + 2 T^{2} )$$
$$3$$$$1 + 3 T + 3 T^{2}$$
$$59$$$$( 1 - T )( 1 + 8 T + 59 T^{2} )$$

Good L-factors:
Prime L-Factor
$$5$$$$( 1 - T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$
$$7$$$$1 + 3 T + 6 T^{2} + 21 T^{3} + 49 T^{4}$$
$$11$$$$( 1 - 6 T + 11 T^{2} )( 1 + 6 T + 11 T^{2} )$$
$$13$$$$1 + 2 T + 10 T^{2} + 26 T^{3} + 169 T^{4}$$
$$17$$$$1 + 2 T - 6 T^{2} + 34 T^{3} + 289 T^{4}$$
$$19$$$$1 + 3 T + 6 T^{2} + 57 T^{3} + 361 T^{4}$$
$$23$$$$1 + 2 T + 10 T^{2} + 46 T^{3} + 529 T^{4}$$
$$29$$$$1 - 3 T + 14 T^{2} - 87 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

See L-function page for more information

## 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.