Genus 2 curves of conductor 576

Results (displaying both matches)

 

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
576.a.576.1	576.a	\( 2^{6} \cdot 3^{2} \)	\( - 2^{6} \cdot 3^{2} \)	$0$	$1$	$\Z/10\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_2$		✓		$C_4$	$D_4$	$4$	$0$	2.180.4, 3.1080.16	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(22.396252\)	\(0.223963\)	$[68,124,2616,72]$	$[68,110,-36,-3637,576]$	$[22717712/9,540430/9,-289]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
576.b.147456.1	576.b	\( 2^{6} \cdot 3^{2} \)	\( - 2^{14} \cdot 3^{2} \)	$0$	$2$	$\Z/4\Z\oplus\Z/4\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathrm{M}_2(\Q)\)		$E_1$				$D_4$	$D_4$	$4$	$0$	2.180.7, 3.2160.25	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(9.301119\)	\(0.290660\)	$[152,109,5469,18]$	$[608,14240,405504,10942208,147456]$	$[5071050752/9,195344320/9,1016576]$	$y^2 = x^6 + 2x^4 + 2x^2 + 1$