Genus 2 curves in isogeny class 1180.a of discriminant 18880

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
1180.a.18880.1	1180.a	\( 2^{2} \cdot 5 \cdot 59 \)	\( - 2^{6} \cdot 5 \cdot 59 \)	$0$	$1$	$\Z/18\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1, 3.80.1	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(24.170512\)	\(0.447602\)	$[916,23257,5960477,-2416640]$	$[229,1216,6656,11392,-18880]$	$[-629763392149/18880,-228170791/295,-5453864/295]$	$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 + 2x$