# Properties

 Label 5449.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 5449.b

Label Equation
5449.b.5449.1 $$y^2 + (x^3 + x + 1)y = x^4 + 2x^3 + x^2$$

## L-function data

Analytic rank:$$2$$

Prime L-Factor
$$5449$$$$( 1 + T )( 1 - 14 T + 5449 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$$
$$3$$$$( 1 + T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$$
$$5$$$$( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$
$$7$$$$1 + 2 T + 12 T^{2} + 14 T^{3} + 49 T^{4}$$
$$11$$$$( 1 + 2 T + 11 T^{2} )( 1 + 6 T + 11 T^{2} )$$
$$13$$$$1 + 5 T + 14 T^{2} + 65 T^{3} + 169 T^{4}$$
$$17$$$$1 + 2 T - 2 T^{2} + 34 T^{3} + 289 T^{4}$$
$$19$$$$( 1 - 2 T + 19 T^{2} )( 1 + 6 T + 19 T^{2} )$$
$$23$$$$1 + 2 T - 16 T^{2} + 46 T^{3} + 529 T^{4}$$
$$29$$$$1 - 2 T - 14 T^{2} - 58 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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