Genus 2 curves in isogeny class 10040.b of discriminant 321280

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.b.321280.1	10040.b	\( 2^{3} \cdot 5 \cdot 251 \)	\( - 2^{8} \cdot 5 \cdot 251 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$8$	$2$	2.30.3	✓	✓	$1$	\( 2 \cdot 7 \)	\(0.018737\)	\(16.510273\)	\(1.082736\)	$[776,8044,1792988,-1285120]$	$[388,4932,80484,1725792,-321280]$	$[-34349361028/1255,-1125325809/1255,-189318489/5020]$	$y^2 + (x + 1)y = 2x^5 - x^4 - 3x^3 + x^2 + x$