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

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.862.1	862.a	\( 2 \cdot 431 \)	\( - 2 \cdot 431 \)	$0$	$1$	$\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$2$	$0$	2.15.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(23.926605\)	\(0.373853\)	$[1940,2609665,270472593,-110336]$	$[485,-98935,11156681,-1094285985,-862]$	$[-26835438303125/862,11286912906875/862,-2624330288225/862]$	$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5$