Genus 2 curves of conductor 1369

Results (displaying both matches)

 

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
1369.a.1369.1	1369.a	\( 37^{2} \)	\( 37^{2} \)	$1$	$1$	$\Z/3\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.30.2, 3.2160.21	✓	✓	$1$	\( 1 \)	\(0.102223\)	\(19.550666\)	\(0.222058\)	$[24,-300,-2976,-5476]$	$[12,56,168,-280,-1369]$	$[-248832/1369,-96768/1369,-24192/1369]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^3 - x^2$
1369.a.50653.1	1369.a	\( 37^{2} \)	\( 37^{3} \)	$1$	$1$	$\Z/3\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.30.4, 3.2160.20	✓	✓	$1$	\( 3 \)	\(0.102223\)	\(6.516889\)	\(0.222058\)	$[456,11220,2199936,202612]$	$[228,296,-98568,-5640280,50653]$	$[616132666368/50653,94818816/1369,-3742848/37]$	$y^2 + x^3y = 2x^5 - 5x^4 + 7x^3 - 6x^2 + 3x - 1$