Genus 2 curve search results

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
686.a.686.1	686.a	\( 2 \cdot 7^{3} \)	\( 2 \cdot 7^{3} \)	$0$	$1$	$\Z/6\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$2$	2.90.3, 3.2160.5	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(11.491655\)	\(0.319213\)	$[420,4305,640185,87808]$	$[105,280,-980,-45325,686]$	$[37209375/2,472500,-15750]$	$y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$