Genus 2 curves of conductor 2916

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
2916.a.5832.1	2916.a	\( 2^{2} \cdot 3^{6} \)	\( 2^{3} \cdot 3^{6} \)	$0$	$0$	$\Z/3\Z\oplus\Z/3\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$D_6$	$4$	$0$	2.60.2, 3.17280.1	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(19.520681\)	\(0.722988\)	$[4,369,1257,-3072]$	$[3,-138,-356,-5028,-5832]$	$[-1/24,23/36,89/162]$	$y^2 + (x^3 + 1)y = x^3$
2916.a.139968.1	2916.a	\( 2^{2} \cdot 3^{6} \)	\( - 2^{6} \cdot 3^{7} \)	$0$	$0$	$\Z/3\Z\oplus\Z/9\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$C_2^2$	$6$	$0$	2.60.2, 3.5760.3	✓	✓	$1$	\( 3^{3} \)	\(1.000000\)	\(19.520681\)	\(0.722988\)	$[324,12609,1778337,73728]$	$[243,-2268,-314496,-20391588,139968]$	$[387420489/64,-3720087/16,-132678]$	$y^2 + (x^2 + x + 1)y = x^6 - 3x^5 + 5x^4 - 6x^3 + x$
2916.b.11664.1	2916.b	\( 2^{2} \cdot 3^{6} \)	\( - 2^{4} \cdot 3^{6} \)	$0$	$0$	$\Z/3\Z\oplus\Z/3\Z$	\(\mathrm{M}_2(\mathsf{CM})\)	\(\Q \times \Q\)	✓	$D_{3,2}$				$C_2^2$	$C_3:D_4$	$4$	$0$	2.60.2, 3.17280.1	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(17.695032\)	\(0.655372\)	$[40,45,555,6]$	$[120,330,-320,-36825,11664]$	$[6400000/3,440000/9,-32000/81]$	$y^2 + y = x^6$