Genus 2 curves in isogeny class 278784.a of discriminant 557568

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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
278784.a.557568.1	278784.a	\( 2^{8} \cdot 3^{2} \cdot 11^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 11^{2} \)	$0$	$2$	$\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$D_4$	$0$	$0$	2.90.5, 3.1080.10			$2$	\( 1 \)	\(1.000000\)	\(5.710508\)	\(2.855254\)	$[1592,1189,630369,2178]$	$[3184,419240,73041408,14200416368,557568]$	$[\frac{639139022845952}{1089},\frac{26430898598080}{1089},1328059136]$	$y^2 + y = 6x^6 - 8x^4 + 4x^2 - 1$

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