Genus 2 curve search results

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
13689.a.13689.1	13689.a	\( 3^{4} \cdot 13^{2} \)	\( 3^{4} \cdot 13^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$12$	$0$	2.80.1, 3.480.12	✓	✓	$1$	\( 1 \)	\(0.017079\)	\(22.369055\)	\(0.382039\)	$[516,8073,1250613,1752192]$	$[129,357,-347,-43053,13689]$	$[441025329/169,9461333/169,-641603/1521]$	$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 4x^3 - 2x^2$
13689.b.13689.1	13689.b	\( 3^{4} \cdot 13^{2} \)	\( 3^{4} \cdot 13^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$3$	$3$	2.240.1, 3.480.12	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(22.369055\)	\(1.398066\)	$[516,8073,1250613,1752192]$	$[129,357,-347,-43053,13689]$	$[441025329/169,9461333/169,-641603/1521]$	$y^2 + (x^2 + x)y = x^5 + 3x^4 + x^3 - 2x^2 - x$