Genus 2 curves in isogeny class 3584.c of discriminant 458752

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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
3584.c.458752.1	3584.c	\( 2^{9} \cdot 7 \)	\( 2^{16} \cdot 7 \)	$0$	$2$	$\Z/4\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$0$	$0$	2.45.1, 3.2160.9			$2$	\( 2 \)	\(1.000000\)	\(3.475514\)	\(0.868879\)	$[828,16635,5308452,56]$	$[3312,279616,-54648832,-64795509760,458752]$	$[6080953884912/7,155007628668/7,-1306723104]$	$y^2 + x^3y = x^6 - 4x^5 - 13x^4 - 22x^3 - 21x^2 - 12x - 4$

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