Genus 2 curves in isogeny class 604.a of discriminant 9664

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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
604.a.9664.1	604.a	\( 2^{2} \cdot 151 \)	\( 2^{6} \cdot 151 \)	$0$	$0$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1, 3.720.5	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(0.291788\)	\(0.291788\)	$[49556,-797087975,-23996873337603,1236992]$	$[12389,39607304,223396249616,299729401586052,9664]$	$[\frac{291864493641401980949}{9664},\frac{9414430497536890397}{1208},\frac{2143030742187944921}{604}]$	$y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$
604.a.9664.2	604.a	\( 2^{2} \cdot 151 \)	\( 2^{6} \cdot 151 \)	$0$	$0$	$\Z/27\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1, 3.80.1	✓	✓	$1$	\( 3^{2} \)	\(1.000000\)	\(23.634831\)	\(0.291788\)	$[116,6265,95277,1236992]$	$[29,-226,836,-6708,9664]$	$[\frac{20511149}{9664},-\frac{2755957}{4832},\frac{175769}{2416}]$	$y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$

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