Genus 2 curves in isogeny class 1083.a of discriminant 1083

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
1083.a.1083.1	1083.a	\( 3 \cdot 19^{2} \)	\( - 3 \cdot 19^{2} \)	$1$	$1$	$\Z/3\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.15.2, 3.720.4	✓	✓	$1$	\( 1 \)	\(0.075149\)	\(22.662454\)	\(0.189229\)	$[56,244,928,4332]$	$[28,-8,264,1832,1083]$	$[17210368/1083,-175616/1083,68992/361]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^3$