Genus 2 curves in isogeny class 720.b of discriminant 116640

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
720.b.116640.1	720.b	\( 2^{4} \cdot 3^{2} \cdot 5 \)	\( 2^{5} \cdot 3^{6} \cdot 5 \)	$0$	$2$	$\Z/2\Z\oplus\Z/12\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$2$	2.180.3, 3.720.4	✓	✓	$1$	\( 2^{2} \cdot 3 \)	\(1.000000\)	\(14.457058\)	\(0.301189\)	$[35416,45688,537039964,466560]$	$[17708,13057938,12831384960,14177105014959,116640]$	$[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$	$y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$