Genus 2 curves in isogeny class 16034.a of discriminant 32068

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
16034.a.32068.1	16034.a	\( 2 \cdot 8017 \)	\( 2^{2} \cdot 8017 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$14$	$0$		✓	✓	$1$	\( 2 \)	\(0.012634\)	\(18.780890\)	\(0.474559\)	$[460,4297,917851,-4104704]$	$[115,372,-3508,-135451,-32068]$	$[-20113571875/32068,-141441375/8017,11598325/8017]$	$y^2 + (x^3 + 1)y = x^5 + x^4 + x^3 + x^2 - x$