Genus 2 curves in isogeny class 360.a of discriminant 6480

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
360.a.6480.1	360.a	\( 2^{3} \cdot 3^{2} \cdot 5 \)	\( 2^{4} \cdot 3^{4} \cdot 5 \)	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$4$	2.360.2, 3.90.1	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(24.163379\)	\(0.188776\)	$[2360,11992,9047820,25920]$	$[1180,56018,3453120,234166319,6480]$	$[28596971960000/81,1150492082200/81,6677950400/9]$	$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$