Genus 2 curve search results

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
864.a.1728.1	864.a	\( 2^{5} \cdot 3^{3} \)	\( - 2^{6} \cdot 3^{3} \)	$0$	$1$	$\Z/12\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$0$	2.90.4, 3.720.4	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(18.142966\)	\(0.377978\)	$[96,180,5256,216]$	$[96,264,576,-3600,1728]$	$[4718592,135168,3072]$	$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$
2592.b.419904.1	2592.b	\( 2^{5} \cdot 3^{4} \)	\( 2^{6} \cdot 3^{8} \)	$0$	$1$	$\Z/12\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$0$	2.90.2, 3.720.4	✓	✓	$1$	\( 2^{2} \cdot 3 \)	\(1.000000\)	\(8.188197\)	\(0.682350\)	$[96,180,5256,216]$	$[288,2376,15552,-291600,419904]$	$[4718592,135168,3072]$	$y^2 + x^3y = 2x^3 - 6x^2 + 6x - 2$