Genus 2 curves in isogeny class 640.a of discriminant 81920

Results (displaying both matches)

 

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
640.a.81920.1	640.a	\( 2^{7} \cdot 5 \)	\( - 2^{14} \cdot 5 \)	$0$	$1$	$\Z/12\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$0$	2.90.1, 3.2160.5	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(7.405674\)	\(0.308570\)	$[912,147,44562,10]$	$[3648,552928,111431680,25193348864,81920]$	$[39432490647552/5,1638374321664/5,18102076416]$	$y^2 + x^3y = 3x^4 + 13x^2 + 20$
640.a.81920.2	640.a	\( 2^{7} \cdot 5 \)	\( 2^{14} \cdot 5 \)	$0$	$1$	$\Z/12\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$2$	2.90.3, 3.2160.5	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(7.405674\)	\(0.308570\)	$[912,147,44562,10]$	$[3648,552928,111431680,25193348864,81920]$	$[39432490647552/5,1638374321664/5,18102076416]$	$y^2 + x^3y = -3x^4 + 13x^2 - 20$