Genus 2 curves in isogeny class 65536.a of discriminant 65536

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
65536.a.65536.1	65536.a	\( 2^{16} \)	\( 2^{16} \)	$1$	$2$	$\Z/2\Z$	\(\mathrm{M}_2(\mathsf{CM})\)	\(\Q \times \Q\)	✓	$D_{2,1}$				$C_2^2$	$GL(2,3)$	$2$	$2$	2.180.5, 3.6480.21	✓	✓	$1$	\( 1 \)	\(0.960252\)	\(8.973176\)	\(2.154127\)	$[20,-20,-40,8]$	$[80,480,-1280,-83200,65536]$	$[50000,3750,-125]$	$y^2 = x^5 + x$