Genus 2 curves of conductor 56629

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
56629.a.56629.1	56629.a	\( 56629 \)	\( 56629 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$16$	$0$		✓	✓	$1$	\( 1 \)	\(0.049000\)	\(14.841003\)	\(0.727209\)	$[460,10153,1182123,-7248512]$	$[115,128,616,13614,-56629]$	$[-20113571875/56629,-194672000/56629,-8146600/56629]$	$y^2 + (x^2 + x + 1)y = x^6 - x^2$
56629.b.56629.1	56629.b	\( 56629 \)	\( 56629 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$8$	$0$		✓	✓	$1$	\( 1 \)	\(0.075093\)	\(12.385246\)	\(0.930050\)	$[240,84,-12792,226516]$	$[120,586,5888,90791,56629]$	$[24883200000/56629,1012608000/56629,84787200/56629]$	$y^2 + x^3y = -2x^2 - 3x - 1$