Genus 2 curves in isogeny class 1239.a of discriminant 8673

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
1239.a.8673.1	1239.a	\( 3 \cdot 7 \cdot 59 \)	\( 3 \cdot 7^{2} \cdot 59 \)	$0$	$1$	$\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1, 3.80.1	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(8.456793\)	\(0.469822\)	$[500,4273,628857,1110144]$	$[125,473,1969,5599,8673]$	$[30517578125/8673,923828125/8673,30765625/8673]$	$y^2 + (x^2 + x + 1)y = -x^6 - x^2 - x$