Genus 2 curves of conductor 10082

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
10082.a.20164.1	10082.a	\( 2 \cdot 71^{2} \)	\( - 2^{2} \cdot 71^{2} \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 2 \)	\(0.137571\)	\(14.062445\)	\(0.967292\)	$[484,-25631,-3305263,-2580992]$	$[121,1678,14112,-277033,-20164]$	$[-25937424601/20164,-1486339679/10082,-51653448/5041]$	$y^2 + (x^2 + x)y = -x^5 + x^3 - 2x^2 - x + 1$