# Properties

 Label 1383.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 1383.a

Label Equation
1383.a.4149.1 $$y^2 + y = x^5 + x^4$$

## L-function data

Analytic rank:$$1$$

Prime L-Factor
$$3$$$$( 1 - T )( 1 + 3 T + 3 T^{2} )$$
$$461$$$$( 1 + T )( 1 - 12 T + 461 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$$
$$5$$$$1 + T + 3 T^{2} + 5 T^{3} + 25 T^{4}$$
$$7$$$$1 + 6 T + 20 T^{2} + 42 T^{3} + 49 T^{4}$$
$$11$$$$1 - 8 T^{2} + 121 T^{4}$$
$$13$$$$( 1 - 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$
$$17$$$$1 - 5 T + 37 T^{2} - 85 T^{3} + 289 T^{4}$$
$$19$$$$1 + T - 15 T^{2} + 19 T^{3} + 361 T^{4}$$
$$23$$$$1 + 3 T - 3 T^{2} + 69 T^{3} + 529 T^{4}$$
$$29$$$$1 + 2 T + 12 T^{2} + 58 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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