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	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(22.396252\)	\(0.223963\)	$[68,124,2616,72]$	$[68,110,-36,-3637,576]$	$[22717712/9,540430/9,-289]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
589824.a.589824.1	589824.a	\( 2^{16} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{2} \)	$0$	$1$	$\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$2$	2.180.5, 3.1080.10	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(13.759439\)	\(3.439860\)	$[68,124,2616,72]$	$[272,1760,-2304,-931072,589824]$	$[22717712/9,540430/9,-289]$	$y^2 = x^5 - 4x^3 + x$
589824.b.589824.1	589824.b	\( 2^{16} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{2} \)	$2$	$3$	$\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$2$	2.180.5, 3.1080.10	✓	✓	$1$	\( 1 \)	\(2.544094\)	\(6.879720\)	\(4.375664\)	$[68,124,2616,72]$	$[272,1760,-2304,-931072,589824]$	$[22717712/9,540430/9,-289]$	$y^2 = x^5 + 4x^3 + x$