Genus 2 curves of conductor 27889

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
27889.a.27889.1	27889.a	\( 167^{2} \)	\( 167^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$4$	$0$	2.12.2, 3.72.2	✓	✓	$1$	\( 1 \)	\(0.124824\)	\(7.332672\)	\(0.915295\)	$[260,7921,884361,3569792]$	$[65,-154,-5688,-98359,27889]$	$[1160290625/27889,-42292250/27889,-24031800/27889]$	$y^2 + (x^3 + x + 1)y = x^5 - x^2 - x - 1$