Genus 2 curves in isogeny class 587.a of discriminant 587

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
587.a.587.1	587.a	\( 587 \)	\( 587 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	\( 1 \)	\(0.003773\)	\(29.510964\)	\(0.111352\)	$[60,1401,54147,-75136]$	$[15,-49,-501,-2479,-587]$	$[-759375/587,165375/587,112725/587]$	$y^2 + (x^3 + x + 1)y = -x^2 - x$