Genus 2 curves of conductor 10137

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
10137.a.10137.1	10137.a	\( 3 \cdot 31 \cdot 109 \)	\( 3 \cdot 31 \cdot 109 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.20.2	✓	✓	$1$	\( 1 \)	\(0.057474\)	\(12.967735\)	\(0.745306\)	$[2628,3417,2633517,1297536]$	$[657,17843,645873,26491478,10137]$	$[40804268165019/3379,1686718970433/3379,92930144859/3379]$	$y^2 + (x^3 + x + 1)y = -2x^4 + 4x^2 - x - 4$