Genus 2 curves of conductor 10130

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
10130.a.162080.1	10130.a	\( 2 \cdot 5 \cdot 1013 \)	\( 2^{5} \cdot 5 \cdot 1013 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.134122\)	\(5.992174\)	\(0.803683\)	$[2144,5248,3753415,648320]$	$[1072,47008,2695089,169845836,162080]$	$[44240899506176/5065,1809698189312/5065,96786036168/5065]$	$y^2 + (x^3 + x^2)y = -x^4 + 3x^2 - 5x - 10$