One refined passport of genus 9 with automorphism group $D_{18}$

• Label: 9.36-4.0.2-2-2-18.1
• Genus: \(9\)
• Quotient genus: \(0\)
• Group: \(D_{18}\)
• Signature: \([ 0; 2, 2, 2, 18 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$9$
Quotient genus:	$0$
Group name:	$D_{18}$
Group identifier:	$[36,4]$
Signature:	$[ 0; 2, 2, 2, 18 ]$

Conjugacy classes for this refined passport:

$2, 3, 3, 10$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{3}^{2}$
Corresponding character(s):	$2, 5, 7$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18) (19,28) (20,29) (21,30) (22,31) (23,32) (24,33) (25,34) (26,35) (27,36)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x(x^{18}+a_{1}x^{9}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.36-4.0.2-2-2-18.1.1

	(1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18) (19,28) (20,29) (21,30) (22,31) (23,32) (24,33) (25,34) (26,35) (27,36)
	(1,19) (2,21) (3,20) (4,26) (5,25) (6,27) (7,23) (8,22) (9,24) (10,28) (11,30) (12,29) (13,35) (14,34) (15,36) (16,32) (17,31) (18,33)
	(1,26) (2,25) (3,27) (4,23) (5,22) (6,24) (7,20) (8,19) (9,21) (10,35) (11,34) (12,36) (13,32) (14,31) (15,33) (16,29) (17,28) (18,30)
	(1,13,7,12,6,18,2,14,8,10,4,16,3,15,9,11,5,17) (19,31,25,30,24,36,20,32,26,28,22,34,21,33,27,29,23,35)