Genus 2 curves in isogeny class 10102.a of discriminant 323264

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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
10102.a.323264.1	10102.a	\( 2 \cdot 5051 \)	\( - 2^{6} \cdot 5051 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$8$	$2$	2.30.3	✓	✓	$1$	\( 2 \cdot 3 \)	\(0.025482\)	\(17.571527\)	\(0.671647\)	$[472,8644,1089623,-1293056]$	$[236,880,3801,30659,-323264]$	$[-\frac{11438788784}{5051},-\frac{180733520}{5051},-\frac{13231281}{20204}]$	$y^2 + (x + 1)y = -x^5 + 3x^4 + x^3 - 3x^2$

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