Genus 2 curves in isogeny class 62208.n of discriminant 746496

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
62208.n.746496.1	62208.n	\( 2^{8} \cdot 3^{5} \)	\( 2^{10} \cdot 3^{6} \)	$0$	$1$	$\Z/6\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_6)$		✓		$C_2$	$D_6$	$3$	$1$	2.120.1, 3.2880.3	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(8.616344\)	\(1.436057\)	$[142,1368,47940,-12]$	$[852,-2586,-2596,-2224797,-746496]$	$[-1804229351/3,154259641/72,3271609/1296]$	$y^2 = x^6 - 3x^3 + 2$