Genus 2 curves in isogeny class 1083.a of discriminant 20577

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.20577.1	1083.a	\( 3 \cdot 19^{2} \)	\( 3 \cdot 19^{3} \)	$1$	$1$	$\Z/3\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.15.2, 3.2160.20	✓	✓	$1$	\( 3 \)	\(0.075149\)	\(7.554151\)	\(0.189229\)	$[904,13684,4578992,82308]$	$[452,6232,-8664,-10688488,20577]$	$[18866536236032/20577,30289293824/1083,-1634432/19]$	$y^2 + x^3y = x^5 - 5x^4 + 11x^3 - 13x^2 + 9x - 3$