Genus 2 curves in isogeny class 9585.a of discriminant 86265

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
9585.a.86265.1	9585.a	\( 3^{3} \cdot 5 \cdot 71 \)	\( - 3^{5} \cdot 5 \cdot 71 \)	$2$	$3$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$14$	$0$	2.15.1	✓	✓	$1$	\( 3 \)	\(0.033545\)	\(17.208694\)	\(0.432943\)	$[1260,9,6592635,11041920]$	$[315,4134,-19180,-5782914,86265]$	$[2552563125/71,106347150/71,-4699100/213]$	$y^2 + (x^3 + 1)y = -2x^4 + 3x^3 - 3x^2 + 2$