Genus 2 curves in isogeny class 8649.a of discriminant 233523

Results (unique match)

 

Label	Class	Conductor	Discriminant	Rank*	2-Selmer rank	Torsion	$\textrm{End}^0(J_{\overline\Q})$	$\textrm{End}^0(J)$	$\GL_2\textsf{-type}$	Sato-Tate	Nonmaximal primes	$\Q$-simple	\(\overline{\Q}\)-simple	\(\Aut(X)\)	\(\Aut(X_{\overline{\Q}})\)	$\Q$-points	$\Q$-Weierstrass points	mod-$\ell$ images	Locally solvable	Square Ш*	Analytic Ш*	Tamagawa	Regulator	Real period	Leading coefficient	Igusa-Clebsch invariants	Igusa invariants	G2-invariants	Equation
8649.a.233523.1	8649.a	\( 3^{2} \cdot 31^{2} \)	\( 3^{5} \cdot 31^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$8$	$0$	2.15.2, 3.432.4	✓	✓	$1$	\( 2 \)	\(0.018739\)	\(9.071150\)	\(0.339965\)	$[36388,-1141271,-13820841051,29890944]$	$[9097,3495695,1814445117,1071530924081,233523]$	$[62300419867534985257/233523,2631649929116327735/233523,1853767256362813/2883]$	$y^2 + (x^3 + x + 1)y = -3x^4 + 3x^3 + 7x^2 - 47x - 70$