Genus 2 curves in isogeny class 20736.a of discriminant 20736

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
20736.a.20736.1	20736.a	\( 2^{8} \cdot 3^{4} \)	\( 2^{8} \cdot 3^{4} \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_3$		✓		$C_6$	$D_6$	$3$	$3$	2.240.1, 3.960.8	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(14.923707\)	\(0.932732\)	$[78,216,4806,81]$	$[156,438,-428,-64653,20736]$	$[4455516,160381/2,-18083/36]$	$y^2 = x^5 + x^4 - 3x^3 - 4x^2 - x$