Genus 2 curves in isogeny class 83422.a of discriminant 166844

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
83422.a.166844.1	83422.a	\( 2 \cdot 53 \cdot 787 \)	\( 2^{2} \cdot 53 \cdot 787 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$18$	$0$		✓	✓	$1$	\( 2 \)	\(0.025289\)	\(16.098251\)	\(0.814204\)	$[876,12345,4168563,-21356032]$	$[219,1484,-2292,-676051,-166844]$	$[-503756397099/166844,-73524213/787,27481653/41711]$	$y^2 + (x^3 + 1)y = -x^5 + x^4 + x^2 - 7x + 6$