Genus 2 curves in isogeny class 713.b of discriminant 713

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
713.b.713.1	713.b	\( 23 \cdot 31 \)	\( 23 \cdot 31 \)	$0$	$0$	$\Z/9\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.20.2, 3.80.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(23.149881\)	\(0.285801\)	$[92,73,6379,-91264]$	$[23,19,-41,-326,-713]$	$[-279841/31,-10051/31,943/31]$	$y^2 + (x^3 + x + 1)y = -x^4$