Genus 2 curves of conductor 1152

Results (unique match)

 

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
1152.a.147456.1	1152.a	\( 2^{7} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{2} \)	$0$	$1$	$\Z/8\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$D_4$	$4$	$2$	2.180.5, 3.1080.10	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(7.270694\)	\(0.454418\)	$[152,109,5469,18]$	$[608,14240,405504,10942208,147456]$	$[5071050752/9,195344320/9,1016576]$	$y^2 = x^6 - 2x^4 + 2x^2 - 1$