Genus 2 curves in isogeny class 6544.b of discriminant 418816

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
6544.b.418816.1	6544.b	\( 2^{4} \cdot 409 \)	\( 2^{10} \cdot 409 \)	$0$	$0$	$\Z/13\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,13$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1	✓	✓	$1$	\( 13 \)	\(1.000000\)	\(14.196880\)	\(1.092068\)	$[152,9748,354156,-1675264]$	$[76,-1384,-4036,-555548,-418816]$	$[-2476099/409,1186607/818,364249/6544]$	$y^2 + (x^3 + x)y = x^5 + 2x^2 + x + 1$