Genus 2 curves in isogeny class 6081.b of discriminant 164187

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
6081.b.164187.1	6081.b	\( 3 \cdot 2027 \)	\( 3^{4} \cdot 2027 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$16$	$0$		✓	✓	$1$	\( 2^{2} \)	\(0.003504\)	\(20.379079\)	\(0.285654\)	$[804,62697,11560485,21015936]$	$[201,-929,4093,-10087,164187]$	$[4050375321/2027,-279408827/6081,18373477/18243]$	$y^2 + (x^3 + x^2 + 1)y = -2x^4 - 5x^3 + 5x + 2$