Genus 2 curves in isogeny class 10016.a of discriminant 641024

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
10016.a.641024.1	10016.a	\( 2^{5} \cdot 313 \)	\( 2^{11} \cdot 313 \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$2$	$2$	2.180.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(3.556106\)	\(0.889027\)	$[7540,280537,678288235,80128]$	$[7540,2181792,781060880,282245675984,641024]$	$[23798893892678125/626,456664687571625/313,173455315333625/2504]$	$y^2 + xy = 8x^5 - 13x^4 - 19x^3 + 9x^2 - x$