Genus 2 curves in isogeny class 12544.c of discriminant 12544

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
12544.c.12544.1	12544.c	\( 2^{8} \cdot 7^{2} \)	\( 2^{8} \cdot 7^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$3$	$3$	2.240.1, 3.480.12	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(21.839889\)	\(1.364993\)	$[62,112,2114,49]$	$[124,342,-332,-39533,12544]$	$[114516604/49,5094261/98,-79763/196]$	$y^2 = x^5 - 2x^4 - x^3 + 3x^2 - x$