Genus 2 curves in isogeny class 20736.i of discriminant 373248

Results (unique match)

 

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
20736.i.373248.1	20736.i	\( 2^{8} \cdot 3^{4} \)	\( 2^{9} \cdot 3^{6} \)	$0$	$1$	$\Z/6\Z$	\(\mathrm{M}_2(\mathsf{CM})\)	\(\Q \times \Q\)	✓	$D_{2,1}$				$C_2^2$	$C_3:D_4$	$2$	$0$	2.180.4, 3.8640.8	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(7.223967\)	\(1.203994\)	$[40,45,555,6]$	$[240,1320,-2560,-589200,373248]$	$[6400000/3,440000/9,-32000/81]$	$y^2 + x^3y = -2$