Genus 2 curves in isogeny class 1311.a of discriminant 814131

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
1311.a.814131.1	1311.a	\( 3 \cdot 19 \cdot 23 \)	\( - 3^{4} \cdot 19 \cdot 23^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(13.753499\)	\(0.429797\)	$[600,2040,860349,3256524]$	$[300,3410,-4761,-3264100,814131]$	$[30000000000/10051,3410000000/30153,-10000/19]$	$y^2 + xy = x^5 + 5x^4 + 5x^3 + 4x^2 + x$