Genus 2 curves in isogeny class 1051.b of discriminant 1051

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
1051.b.1051.1	1051.b	\( 1051 \)	\( -1051 \)	$0$	$1$	$\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(23.331720\)	\(0.364558\)	$[64,-200,185,4204]$	$[32,76,-241,-3372,1051]$	$[33554432/1051,2490368/1051,-246784/1051]$	$y^2 + (x + 1)y = -x^5 - x^4$
1051.b.1051.2	1051.b	\( 1051 \)	\( -1051 \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$3$	2.120.3	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(5.832930\)	\(0.364558\)	$[6176,-50240,-103225225,-4204]$	$[3088,405696,72449921,14784027908,-1051]$	$[-280793117300359168/1051,-11946277554880512/1051,-690863899476224/1051]$	$y^2 + xy = x^5 + 8x^4 + 16x^3 + x$