Genus 2 curves in isogeny class 61127.a of discriminant 61127

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
61127.a.61127.1	61127.a	\( 11 \cdot 5557 \)	\( - 11 \cdot 5557 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$18$	$0$		✓	✓	$1$	\( 1 \)	\(0.029475\)	\(19.614389\)	\(0.578137\)	$[548,10489,1460957,-7824256]$	$[137,345,2293,48779,-61127]$	$[-48261724457/61127,-887116785/61127,-43037317/61127]$	$y^2 + (x^3 + x + 1)y = 2x^5 + 3x^4 - x^2$