Genus 2 curves in isogeny class 8192.c of discriminant 524288

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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
8192.c.524288.1	8192.c	\( 2^{13} \)	\( - 2^{19} \)	$1$	$2$	$\Z/2\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$0$	2.90.1, 3.270.2	✓	✓	$1$	\( 2 \)	\(0.216166\)	\(7.483901\)	\(0.808881\)	$[168,39,2121,2]$	$[1344,73600,5275648,418377728,524288]$	$[8364238848,340804800,18176256]$	$y^2 = x^6 + 3x^4 + 4x^2 + 2$
8192.c.524288.2	8192.c	\( 2^{13} \)	\( 2^{19} \)	$1$	$2$	$\Z/2\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$2$	2.90.3, 3.270.2	✓	✓	$1$	\( 2 \)	\(0.216166\)	\(7.483901\)	\(0.808881\)	$[168,39,2121,2]$	$[1344,73600,5275648,418377728,524288]$	$[8364238848,340804800,18176256]$	$y^2 = x^6 - 3x^4 + 4x^2 - 2$

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