Genus 2 curves of conductor 1176

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
1176.a.2352.1	1176.a	\( 2^{3} \cdot 3 \cdot 7^{2} \)	\( - 2^{4} \cdot 3 \cdot 7^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$0$	2.180.7, 3.90.1	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(12.624711\)	\(0.394522\)	$[1032,984,324564,9408]$	$[516,10930,305472,9539663,2352]$	$[762091768512/49,31284414360/49,1694453184/49]$	$y^2 + (x^3 + x)y = x^4 + 3x^2 + 3$
1176.b.16464.1	1176.b	\( 2^{3} \cdot 3 \cdot 7^{2} \)	\( 2^{4} \cdot 3 \cdot 7^{3} \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2$	$C_2$	$4$	$2$	2.180.3, 3.640.2	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(13.019302\)	\(0.361647\)	$[160,4720,130020,-65856]$	$[80,-520,4220,16800,-16464]$	$[-204800000/1029,16640000/1029,-1688000/1029]$	$y^2 + (x + 1)y = -2x^5 + x^2$