Genus 2 curves in isogeny class 100089.a of discriminant 100089

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
100089.a.100089.1	100089.a	\( 3^{3} \cdot 11 \cdot 337 \)	\( 3^{3} \cdot 11 \cdot 337 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$4$	$0$		✓	✓	$1$	\( 1 \)	\(0.106187\)	\(14.805872\)	\(1.572193\)	$[252,11745,848655,-12811392]$	$[63,-324,-2644,-67887,-100089]$	$[-36756909/3707,3000564/3707,388668/3707]$	$y^2 + (x^3 + x + 1)y = -x^5 + x^4 - 2x^2 + x$