Genus 2 curves in isogeny class 277.a of discriminant 277

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	Locally solvable	Square Ш*	Analytic Ш*	Tamagawa	Regulator	Real period	Leading coefficient	Igusa-Clebsch invariants	Igusa invariants	G2-invariants	Equation
277.a.277.1	277.a	\( 277 \)	\( 277 \)	$0$	$0$	$\Z/15\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3,5$	✓	✓	$C_2$	$C_2$	$5$	$1$	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(32.205749\)	\(0.143137\)	$[64,352,9552,-1108]$	$[32,-16,-464,-3776,-277]$	$[-33554432/277,524288/277,475136/277]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x$
277.a.277.2	277.a	\( 277 \)	\( 277 \)	$0$	$0$	$\Z/5\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3,5$	✓	✓	$C_2$	$C_2$	$1$	$1$	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(3.578417\)	\(0.143137\)	$[4480,1370512,1511819744,-1108]$	$[2240,-19352,164384,-1569936,-277]$	$[-56394933862400000/277,217505333248000/277,-824813158400/277]$	$y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$