Genus 2 curves of conductor 100082

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
100082.a.800656.1	100082.a	\( 2 \cdot 163 \cdot 307 \)	\( - 2^{4} \cdot 163 \cdot 307 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$9$	$1$	2.6.1	✓	✓	$1$	\( 2^{2} \)	\(0.026991\)	\(14.653381\)	\(1.582047\)	$[8760,105132,295938975,-3202624]$	$[4380,781828,182944825,47510827979,-800656]$	$[-100751279419800000/50041,-4105949171526000/50041,-219355418795625/50041]$	$y^2 + (x^3 + x)y = -7x^4 + 26x^2 - 29x + 9$