Genus 2 curves in isogeny class 762.a of discriminant 3048

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
762.a.3048.1	762.a	\( 2 \cdot 3 \cdot 127 \)	\( - 2^{3} \cdot 3 \cdot 127 \)	$0$	$1$	$\Z/12\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.15.1, 3.80.1	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(16.733449\)	\(0.348614\)	$[428,3169,355487,390144]$	$[107,345,1823,19009,3048]$	$[14025517307/3048,140879945/1016,20871527/3048]$	$y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$