Genus 2 curves of conductor 59049

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
59049.a.177147.1	59049.a	\( 3^{10} \)	\( 3^{11} \)	$1$	$1$	$\Z/3\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_3)$		✓		$C_2$	$D_6$	$4$	$0$	2.20.3, 3.5760.8	✓	✓	$1$	\( 3 \)	\(0.712785\)	\(8.055321\)	\(1.913904\)	$[52,-63,-111,384]$	$[117,783,-2079,-214083,177147]$	$[371293/3,63713/9,-13013/81]$	$y^2 + (x^3 + 1)y = x^3 - 1$