Genus 2 curves in isogeny class 7396.a of discriminant 29584

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
7396.a.29584.1	7396.a	\( 2^{2} \cdot 43^{2} \)	\( - 2^{4} \cdot 43^{2} \)	$2$	$2$	$\Z/3\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$12$	$0$	2.60.2, 3.720.4	✓	✓	$1$	\( 3 \)	\(0.047749\)	\(21.927407\)	\(0.349006\)	$[56,1285,33089,3698]$	$[56,-726,-15680,-351289,29584]$	$[34420736/1849,-7968576/1849,-3073280/1849]$	$y^2 + y = x^6 - 2x^4 + x^2$