Genus 2 curve search results

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
576.a.576.1	576.a	\( 2^{6} \cdot 3^{2} \)	\( - 2^{6} \cdot 3^{2} \)	$0$	$1$	$\Z/10\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_2$		✓		$C_4$	$D_4$	$4$	$0$	2.180.4, 3.1080.16	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(22.396252\)	\(0.223963\)	$[68,124,2616,72]$	$[68,110,-36,-3637,576]$	$[22717712/9,540430/9,-289]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
69696.c.627264.1	69696.c	\( 2^{6} \cdot 3^{2} \cdot 11^{2} \)	\( - 2^{6} \cdot 3^{4} \cdot 11^{2} \)	$0$	$1$	$\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_2$		✓		$C_4$	$D_4$	$0$	$0$	2.180.4, 3.1080.16		✓	$1$	\( 2 \)	\(1.000000\)	\(7.488051\)	\(3.744026\)	$[1220,3580,1448760,78408]$	$[1220,59630,3724380,247001675,627264]$	$[42229815050000/9801,1691859628750/9801,8837375]$	$y^2 + (x^3 + x^2 + x + 1)y = x^6 + 3x^4 - x^3 + 3x^2 - x + 1$
78400.a.78400.1	78400.a	\( 2^{6} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{6} \cdot 5^{2} \cdot 7^{2} \)	$0$	$2$	$\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_2$		✓		$C_4$	$D_4$	$0$	$0$	2.90.5, 3.1080.16			$2$	\( 1 \)	\(1.000000\)	\(6.009550\)	\(3.004775\)	$[452,1276,189752,9800]$	$[452,7662,151900,2488139,78400]$	$[294789628688/1225,11055476814/1225,395839]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 3x^4 - x^3 - 3x^2 - x - 1$