Genus 2 curves in isogeny class 26244.e of discriminant 472392

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
26244.e.472392.1	26244.e	\( 2^{2} \cdot 3^{8} \)	\( - 2^{3} \cdot 3^{10} \)	$0$	$0$	$\Z/3\Z\oplus\Z/3\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_3)$		✓		$C_2$	$D_6$	$4$	$0$	2.20.3, 3.5760.3	✓	✓	$1$	\( 3^{2} \)	\(1.000000\)	\(12.048083\)	\(1.338676\)	$[356,3969,419553,248832]$	$[267,1482,-2884,-741588,472392]$	$[5584059449/1944,174127343/2916,-5711041/13122]$	$y^2 + (x^3 + 1)y = 2$