Genus 2 curves in isogeny class 100317.a of discriminant 702219

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
100317.a.702219.1	100317.a	\( 3 \cdot 7 \cdot 17 \cdot 281 \)	\( - 3 \cdot 7^{2} \cdot 17 \cdot 281 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	\( 2 \)	\(0.346453\)	\(8.322593\)	\(1.441696\)	$[7032,-686316,-1600461345,-2808876]$	$[3516,629480,166727073,47491829567,-702219]$	$[-179111337635976192/234073,-9120261286863360/234073,-687040919518896/234073]$	$y^2 + (x^2 + 1)y = x^5 - 10x^3 - 10x^2 + 28x + 38$