Properties

 Label 100283.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 100283.a

Label Equation
100283.a.100283.1 $$y^2 + (x^2 + 1)y = x^5 - x^4 - x^3 - x$$

L-function data

Analytic rank:$$2$$

Prime L-Factor
$$17$$$$1 + 2 T + 17 T^{2}$$
$$347$$$$( 1 + T )( 1 - 15 T + 347 T^{2} )$$

Good L-factors:
Prime L-Factor
$$2$$$$1 + T + 2 T^{3} + 4 T^{4}$$
$$3$$$$1 + T + T^{2} + 3 T^{3} + 9 T^{4}$$
$$5$$$$1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$$
$$7$$$$1 + 49 T^{4}$$
$$11$$$$1 + 5 T + 19 T^{2} + 55 T^{3} + 121 T^{4}$$
$$13$$$$1 + 7 T + 27 T^{2} + 91 T^{3} + 169 T^{4}$$
$$19$$$$1 + 4 T + 24 T^{2} + 76 T^{3} + 361 T^{4}$$
$$23$$$$1 + 4 T + 28 T^{2} + 92 T^{3} + 529 T^{4}$$
$$29$$$$1 - 3 T + 36 T^{2} - 87 T^{3} + 841 T^{4}$$
$\cdots$$\cdots$

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