Genus 2 curves in isogeny class 270720.b of discriminant 270720

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
270720.b.270720.1	270720.b	\( 2^{7} \cdot 3^{2} \cdot 5 \cdot 47 \)	\( - 2^{7} \cdot 3^{2} \cdot 5 \cdot 47 \)	$0$	$6$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.90.6, 3.90.1		✓	$16$	\( 1 \)	\(1.000000\)	\(3.383512\)	\(3.383512\)	$[3249520,48397,52421227290,33840]$	$[3249520,439974144002,79428031708101120,16131432551454029721599,270720]$	$[566129906277843097800186880000/423,23588744365074445774311454400/423,3098074718373623337958400]$	$y^2 + xy = 3x^6 + 70x^4 + 544x^2 + 1410$