Genus 2 curves in isogeny class 4388.a of discriminant 140416

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
4388.a.140416.1	4388.a	\( 2^{2} \cdot 1097 \)	\( 2^{7} \cdot 1097 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$0$	2.10.1	✓	✓	$1$	\( 11 \)	\(0.002816\)	\(17.459324\)	\(0.540853\)	$[212,14185,450581,17973248]$	$[53,-474,2788,-19228,140416]$	$[418195493/140416,-35283849/70208,1957873/35104]$	$y^2 + (x^3 + 1)y = -x^5 + 2x^2 - x$