Genus 2 curves in isogeny class 52441.a of discriminant 52441

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
52441.a.52441.1	52441.a	\( 229^{2} \)	\( 229^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$3$	$3$	2.240.1, 3.480.12	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(22.932231\)	\(1.433264\)	$[964,41449,10706437,6712448]$	$[241,693,-683,-161213,52441]$	$[812990017201/52441,9700282053/52441,-39669323/52441]$	$y^2 + (x^2 + x)y = x^5 + 5x^4 + 5x^3 - x$