Genus 2 curves in isogeny class 5580.a of discriminant 33480

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
5580.a.33480.1	5580.a	\( 2^{2} \cdot 3^{2} \cdot 5 \cdot 31 \)	\( 2^{3} \cdot 3^{3} \cdot 5 \cdot 31 \)	$1$	$1$	$\Z/3\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$3$	✓	✓	$C_2$	$C_2$	$10$	$0$	3.80.1	✓	✓	$1$	\( 3^{2} \)	\(0.027041\)	\(20.905602\)	\(0.565312\)	$[388,10417,421321,4285440]$	$[97,-42,7956,192492,33480]$	$[8587340257/33480,-6388711/5580,2079389/930]$	$y^2 + (x^3 + x + 1)y = x^5 - 2x^4 - 2x^3 + x^2$