Genus 2 curves in isogeny class 5200.b of discriminant 332800

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
5200.b.332800.1	5200.b	\( 2^{4} \cdot 5^{2} \cdot 13 \)	\( 2^{10} \cdot 5^{2} \cdot 13 \)	$0$	$0$	$\Z/13\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,13$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1	✓	✓	$1$	\( 13 \)	\(1.000000\)	\(13.486416\)	\(1.037417\)	$[8,316,-10722,41600]$	$[8,-208,10000,9184,332800]$	$[32/325,-8/25,25/13]$	$y^2 + (x + 1)y = x^6 + 2x^5 + 2x^4 - x^2$