Genus 2 curves in isogeny class 961.a of discriminant 923521

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
961.a.923521.1	961.a	\( 31^{2} \)	\( 31^{4} \)	$0$	$0$	$\Z/5\Z$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$2$	$0$	2.120.2, 3.72.2	✓	✓	$1$	\( 5 \)	\(1.000000\)	\(2.246439\)	\(0.449288\)	$[4100,78961,94151689,118210688]$	$[1025,40486,2121888,133954751,923521]$	$[1131408212890625/923521,1406419156250/29791,2319780000/961]$	$y^2 + (x^3 + x^2 + 1)y = -5x^4 + 4x^3 + 3x^2 - 2x - 3$