Genus 2 curve search results

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
1116.a.214272.1	1116.a	\( 2^{2} \cdot 3^{2} \cdot 31 \)	\( - 2^{8} \cdot 3^{3} \cdot 31 \)	$0$	$0$	$\Z/39\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3,13$	✓	✓	$C_2$	$C_2$	$8$	$0$	2.10.1, 3.80.1	✓	✓	$1$	\( 3 \cdot 13 \)	\(1.000000\)	\(16.984099\)	\(0.435490\)	$[52,22201,238285,-27426816]$	$[13,-918,36,-210564,-214272]$	$[-371293/214272,37349/3968,-169/5952]$	$y^2 + (x^3 + 1)y = x^4 + 2x^3 + x^2 - x$