Genus 2 curves in isogeny class 59967.a of discriminant 539703

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
59967.a.539703.1	59967.a	\( 3^{3} \cdot 2221 \)	\( - 3^{5} \cdot 2221 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$20$	$0$		✓	✓	$1$	\( 3 \)	\(0.013599\)	\(14.898743\)	\(0.607808\)	$[20,1281,78353,284288]$	$[15,-471,-27373,-158109,539703]$	$[3125/2221,-19625/6663,-684325/59967]$	$y^2 + (x^3 + x^2 + 1)y = x^4 + 2x^3 - x^2 - 2x$