Genus 2 curves in isogeny class 62563.a of discriminant 62563

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
62563.a.62563.1	62563.a	\( 62563 \)	\( 62563 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$18$	$0$		✓	✓	$1$	\( 1 \)	\(0.029057\)	\(21.403273\)	\(0.621922\)	$[1028,58585,13837773,8008064]$	$[257,311,21365,1348521,62563]$	$[1121154893057/62563,5279098423/62563,1411136885/62563]$	$y^2 + (x^3 + x + 1)y = -3x^4 + x^3 + 3x^2 - x$