Genus 2 curves in isogeny class 10080.b of discriminant 60480

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
10080.b.60480.1	10080.b	\( 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \)	\( - 2^{6} \cdot 3^{3} \cdot 5 \cdot 7 \)	$0$	$3$	$\Z/4\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.90.5, 3.90.1		✓	$4$	\( 2 \)	\(1.000000\)	\(0.944615\)	\(0.472308\)	$[161296,406586887,19127473723714,7560]$	$[161296,812958726,4856153621760,30594066098964471,60480]$	$[1705838896690345318825984/945,17767980154611986862208/315,6266846885932235776/3]$	$y^2 + xy = -15x^6 - 58x^4 - 60x^2 - 7$