Genus 2 curves of conductor 10044

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
10044.a.40176.1	10044.a	\( 2^{2} \cdot 3^{4} \cdot 31 \)	\( - 2^{4} \cdot 3^{4} \cdot 31 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1, 3.90.2	✓	✓	$1$	\( 2 \)	\(0.141330\)	\(13.036036\)	\(0.921192\)	$[108,-6543,-22041,5142528]$	$[27,303,-1693,-34380,40176]$	$[177147/496,73629/496,-15237/496]$	$y^2 + (x^2 + x + 1)y = -x^5 - 2x^2$