Genus 2 curves in isogeny class 862.a of discriminant 6896

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
862.a.6896.1	862.a	\( 2 \cdot 431 \)	\( - 2^{4} \cdot 431 \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(23.926605\)	\(0.373853\)	$[932,12385,3688145,-882688]$	$[233,1746,11456,-94817,-6896]$	$[-686719856393/6896,-11042871201/3448,-38870924/431]$	$y^2 + (x^2 + x)y = 4x^5 + 6x^4 - 3x^2 - x$