One refined passport of genus 8 with automorphism group $D_{18}$

• Label: 8.36-4.0.2-2-2-9.3
• Genus: \(8\)
• Quotient genus: \(0\)
• Group: \(D_{18}\)
• Signature: \([ 0; 2, 2, 2, 9 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$8$
Quotient genus:	$0$
Group name:	$D_{18}$
Group identifier:	$[36,4]$
Signature:	$[ 0; 2, 2, 2, 9 ]$

Conjugacy classes for this refined passport:

$2, 3, 4, 9$

Jacobian variety group algebra decomposition:	$E^{2}\times A_{3}^{2}$
Corresponding character(s):	$5, 8$

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:

$y^2=x^{18}+a_1x^{9}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.36-4.0.2-2-2-9.3.1

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