Genus 2 curves in isogeny class 1055.a of discriminant 1055

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
1055.a.1055.1	1055.a	\( 5 \cdot 211 \)	\( - 5 \cdot 211 \)	$0$	$1$	$\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1, 3.80.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(15.577626\)	\(0.432712\)	$[500,-3023,-525127,-135040]$	$[125,777,7441,81599,-1055]$	$[-6103515625/211,-303515625/211,-23253125/211]$	$y^2 + (x^3 + 1)y = -x^4 + x^2 - x - 1$