Genus 2 curves in isogeny class 8649.a of discriminant 77841

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.77841.1	8649.a	\( 3^{2} \cdot 31^{2} \)	\( 3^{4} \cdot 31^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$14$	$0$	2.120.2, 3.432.4	✓	✓	$1$	\( 2^{2} \)	\(0.004685\)	\(18.142300\)	\(0.339965\)	$[92,17689,603507,-9963648]$	$[23,-715,-3645,-148765,-77841]$	$[-6436343/77841,8699405/77841,23805/961]$	$y^2 + (x^3 + x + 1)y = x^3 + x^2 - 2x$