Genus 2 curves in isogeny class 100162.b of discriminant 400648

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
100162.b.400648.1	100162.b	\( 2 \cdot 61 \cdot 821 \)	\( - 2^{3} \cdot 61 \cdot 821 \)	$1$	$1$	$\Z/3\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1, 3.80.1	✓	✓	$1$	\( 3 \)	\(0.772491\)	\(11.205131\)	\(2.885289\)	$[3652,-232031,-299933231,-51282944]$	$[913,44400,3475524,300448353,-400648]$	$[-634386434595793/400648,-4223819158350/50081,-724272266289/100162]$	$y^2 + (x^2 + x)y = x^5 - 4x^4 + 4x^2 + 5x + 2$