Genus 2 curves in isogeny class 42439.a of discriminant 42439

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
42439.a.42439.1	42439.a	\( 31 \cdot 37^{2} \)	\( - 31 \cdot 37^{2} \)	$3$	$3$	$\mathsf{trivial}$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$14$	$0$	2.15.2, 3.90.1	✓	✓	$1$	\( 1 \)	\(0.029811\)	\(19.960990\)	\(0.595048\)	$[504,3156,671472,169756]$	$[252,2120,-744,-1170472,42439]$	$[1016255020032/42439,33926376960/42439,-1524096/1369]$	$y^2 + y = x^6 - 3x^5 + 3x^4 - x^3 - x^2 + x$