Genus 2 curves of conductor 864

Results (3 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	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(18.142966\)	\(0.377978\)	$[96,180,5256,216]$	$[96,264,576,-3600,1728]$	$[4718592,135168,3072]$	$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$
864.a.221184.1	864.a	\( 2^{5} \cdot 3^{3} \)	\( - 2^{13} \cdot 3^{3} \)	$0$	$1$	$\Z/12\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$0$	2.45.1, 3.720.4	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(18.142966\)	\(0.377978\)	$[168,34560,-211428,-864]$	$[336,-87456,10192896,-1055934720,-221184]$	$[-19361664,14998704,-5202624]$	$y^2 + x^3y = x^5 - 4x^4 - 6x^3 + 33x^2 - 36x + 12$
864.a.442368.1	864.a	\( 2^{5} \cdot 3^{3} \)	\( 2^{14} \cdot 3^{3} \)	$0$	$1$	$\Z/12\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$2$	2.90.3, 3.720.4	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(9.071483\)	\(0.377978\)	$[552,45,7083,54]$	$[2208,202656,24809472,3427464960,442368]$	$[118634674176,4931431104,273421056]$	$y^2 = x^6 - 4x^4 + 6x^2 - 3$