Genus 2 curves of conductor 5599

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
5599.a.5599.1	5599.a	\( 11 \cdot 509 \)	\( 11 \cdot 509 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$12$	$0$		✓	✓	$1$	\( 1 \)	\(0.012163\)	\(21.606456\)	\(0.262794\)	$[28,937,106107,-716672]$	$[7,-37,-1397,-2787,-5599]$	$[-16807/5599,12691/5599,6223/509]$	$y^2 + (x^3 + x + 1)y = -x^4 + x^2 - 2x$