Genus 2 curves of conductor 472

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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
472.a.944.1	472.a	\( 2^{3} \cdot 59 \)	\( - 2^{4} \cdot 59 \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(29.113273\)	\(0.227447\)	$[280,760,60604,-3776]$	$[140,690,4544,40015,-944]$	$[-\frac{3361400000}{59},-\frac{118335000}{59},-\frac{5566400}{59}]$	$y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$
472.a.60416.1	472.a	\( 2^{3} \cdot 59 \)	\( 2^{10} \cdot 59 \)	$0$	$1$	$\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(7.278318\)	\(0.227447\)	$[152,17065,1592025,7552]$	$[152,-10414,-926656,-62325777,60416]$	$[\frac{79235168}{59},-\frac{35714813}{59},-\frac{20907676}{59}]$	$y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$

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