Genus 2 curves in isogeny class 22556.a of discriminant 721792

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
22556.a.721792.1	22556.a	\( 2^{2} \cdot 5639 \)	\( - 2^{7} \cdot 5639 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$14$	$0$	2.10.1	✓	✓	$1$	\( 11 \)	\(0.004973\)	\(16.481143\)	\(0.901630\)	$[468,62745,2790333,-92389376]$	$[117,-2044,49920,415676,-721792]$	$[-21924480357/721792,818424243/180448,-5338710/5639]$	$y^2 + (x^3 + 1)y = 3x^3 + 2x^2 - 2x$