Genus 2 curves in isogeny class 11664.c of discriminant 34992

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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
11664.c.34992.1	11664.c	\( 2^{4} \cdot 3^{6} \)	\( - 2^{4} \cdot 3^{7} \)	$0$	$1$	$\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1, 3.720.4	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(14.025272\)	\(0.779182\)	$[80,-792,-20508,-576]$	$[120,1788,25924,-21516,-34992]$	$[-\frac{6400000}{9},-\frac{2384000}{27},-\frac{2592400}{243}]$	$y^2 + (x + 1)y = -x^6 + 2x^2 + x$

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