Genus 2 curves in isogeny class 784.c of discriminant 614656

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
784.c.614656.1	784.c	\( 2^{4} \cdot 7^{2} \)	\( 2^{8} \cdot 7^{4} \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_3$		✓		$C_6$	$D_6$	$3$	$3$	2.240.1, 3.5760.7	✓	✓	$1$	\( 3^{2} \)	\(1.000000\)	\(5.731485\)	\(0.358218\)	$[398,9016,912086,2401]$	$[796,2358,-2348,-1857293,614656]$	$[1248318403996/2401,9291226221/4802,-23245787/9604]$	$y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$