Genus 2 curves in isogeny class 5547.b of discriminant 16641

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
5547.b.16641.1	5547.b	\( 3 \cdot 43^{2} \)	\( 3^{2} \cdot 43^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$14$	$0$	2.30.2, 3.90.1	✓	✓	$1$	\( 2 \)	\(0.006279\)	\(24.460380\)	\(0.307178\)	$[520,6292,896816,66564]$	$[260,1768,16776,308984,16641]$	$[1188137600000/16641,31074368000/16641,126006400/1849]$	$y^2 + y = x^6 - 3x^5 + x^4 + 3x^3 - x^2 - x$