Genus 2 curves in isogeny class 6336.a of discriminant 152064

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
6336.a.152064.1	6336.a	\( 2^{6} \cdot 3^{2} \cdot 11 \)	\( 2^{9} \cdot 3^{3} \cdot 11 \)	$1$	$1$	$\Z/3\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$10$	$0$	2.10.1, 3.80.1	✓	✓	$1$	\( 2^{2} \cdot 3 \)	\(0.027391\)	\(16.866005\)	\(0.615972\)	$[68,1369,33335,-19008]$	$[68,-720,-11664,-327888,-152064]$	$[-2839714/297,49130/33,7803/22]$	$y^2 + (x^3 + x)y = -x^4 - 2x^3 + 2x + 1$