Genus 2 curves in isogeny class 5769.b of discriminant 17307

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
5769.b.17307.1	5769.b	\( 3^{2} \cdot 641 \)	\( - 3^{3} \cdot 641 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$14$	$0$		✓	✓	$1$	\( 2 \)	\(0.005378\)	\(24.769580\)	\(0.266444\)	$[324,19881,1386405,-2215296]$	$[81,-555,613,-64593,-17307]$	$[-129140163/641,10924065/641,-148959/641]$	$y^2 + (x^3 + x + 1)y = x^5 - 3x^3$