Properties

 Label 841.a Sato-Tate group $G_{3,3}$ $$\End(J_{\overline{\Q}}) \otimes \R$$ $$\R \times \R$$ $$\End(J_{\overline{\Q}}) \otimes \Q$$ $$\mathrm{RM}$$ $$\overline{\Q}$$-simple yes $$\mathrm{GL}_2$$-type yes

Related objects

Genus 2 curves in isogeny class 841.a

Label Equation
841.a.841.1 $$y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2$$

L-function data

Analytic rank:$$0$$

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

Good L-factors:
Prime L-Factor
$$2$$$$1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$$
$$3$$$$1 - 2 T + 5 T^{2} - 6 T^{3} + 9 T^{4}$$
$$5$$$$( 1 + T + 5 T^{2} )^{2}$$
$$7$$$$1 + 6 T^{2} + 49 T^{4}$$
$$11$$$$1 - 2 T + 21 T^{2} - 22 T^{3} + 121 T^{4}$$
$$13$$$$1 + 2 T + 19 T^{2} + 26 T^{3} + 169 T^{4}$$
$$17$$$$1 + 4 T + 30 T^{2} + 68 T^{3} + 289 T^{4}$$
$$19$$$$( 1 - 6 T + 19 T^{2} )^{2}$$
$$23$$$$1 + 4 T + 18 T^{2} + 92 T^{3} + 529 T^{4}$$
$\cdots$$\cdots$

$$\mathrm{ST} =$$ $G_{3,3}$, $$\quad \mathrm{ST}^0 = \mathrm{SU}(2)\times\mathrm{SU}(2)$$
Of $$\GL_2$$-type over $$\Q$$
All $$\overline{\Q}$$-endomorphisms of the Jacobian are defined over $$\Q$$.