Genus 2 curves in isogeny class 834.a of discriminant 1668

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
834.a.1668.1	834.a	\( 2 \cdot 3 \cdot 139 \)	\( 2^{2} \cdot 3 \cdot 139 \)	$0$	$1$	$\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(11.763516\)	\(0.367610\)	$[372,3345,401289,213504]$	$[93,221,-111,-14791,1668]$	$[2318961231/556,59254299/556,-320013/556]$	$y^2 + (x^3 + 1)y = -x^2 + x - 1$