Genus 2 curves in isogeny class 324.a of discriminant 648

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
324.a.648.1	324.a	\( 2^{2} \cdot 3^{4} \)	\( - 2^{3} \cdot 3^{4} \)	$0$	$0$	$\Z/21\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_3$		✓		$C_6$	$D_6$	$6$	$0$	2.40.3, 3.1920.3	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(25.521769\)	\(0.173617\)	$[60,945,2295,82944]$	$[15,-30,140,300,648]$	$[9375/8,-625/4,875/18]$	$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$