Genus 2 curves in isogeny class 971.a of discriminant 971

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
971.a.971.1	971.a	\( 971 \)	\( -971 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.005970\)	\(29.647111\)	\(0.176998\)	$[256,1024,80304,-3884]$	$[128,512,2000,-1536,-971]$	$[-34359738368/971,-1073741824/971,-32768000/971]$	$y^2 + y = x^5 - 2x^3 + x$