Genus 2 curves in isogeny class 1088.b of discriminant 2176

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
1088.b.2176.1	1088.b	\( 2^{6} \cdot 17 \)	\( - 2^{7} \cdot 17 \)	$0$	$1$	$\Z/6\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$0$	2.45.1, 3.2160.5	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(5.893944\)	\(0.491162\)	$[7572,68115,166006308,272]$	$[7572,2343556,952909568,430794130940,2176]$	$[194465720403941544/17,7948719687495546/17,25108109106912]$	$y^2 + (x^3 + x)y = 4x^4 + 24x^2 + 34$
1088.b.2176.2	1088.b	\( 2^{6} \cdot 17 \)	\( 2^{7} \cdot 17 \)	$0$	$1$	$\Z/12\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$0$	2.90.1, 3.2160.5	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(23.575776\)	\(0.491162\)	$[7572,68115,166006308,272]$	$[7572,2343556,952909568,430794130940,2176]$	$[194465720403941544/17,7948719687495546/17,25108109106912]$	$y^2 + (x^3 + x)y = -5x^4 + 24x^2 - 34$