Genus 2 curves in isogeny class 10040.c of discriminant 502000

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
10040.c.502000.1	10040.c	\( 2^{3} \cdot 5 \cdot 251 \)	\( - 2^{4} \cdot 5^{3} \cdot 251 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$6$	$2$	2.30.3	✓	✓	$1$	\( 2 \cdot 3 \)	\(0.045172\)	\(11.060477\)	\(0.749431\)	$[16,-4076,38588,2008000]$	$[8,682,-5796,-127873,502000]$	$[2048/31375,21824/31375,-23184/31375]$	$y^2 + (x^2 + 1)y = x^5 - 3x^4 + 3x^3 - 2x$