Genus 2 curves of conductor 80533

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
80533.a.80533.1	80533.a	\( 29 \cdot 2777 \)	\( 29 \cdot 2777 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.105287\)	\(11.105185\)	\(1.169235\)	$[352,580,52279,322132]$	$[176,1194,11537,151219,80533]$	$[168874213376/80533,6509420544/80533,357370112/80533]$	$y^2 + (x^3 + x^2)y = -2x^2 - 5x - 3$