Genus 2 curves in isogeny class 2588.a of discriminant 82816

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
2588.a.82816.1	2588.a	\( 2^{2} \cdot 647 \)	\( - 2^{7} \cdot 647 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	\( 11 \)	\(0.002169\)	\(17.413917\)	\(0.415511\)	$[12,9465,-98157,10600448]$	$[3,-394,1692,-37540,82816]$	$[243/82816,-5319/41408,3807/20704]$	$y^2 + (x^3 + 1)y = x^3 + 2x^2$