One refined passport of genus 8 with automorphism group $C_9:D_4$

• Label: 8.72-8.0.2-4-18.1
• Genus: \(8\)
• Quotient genus: \(0\)
• Group: \(C_9:D_4\)
• Signature: \([ 0; 2, 4, 18 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$8$
Quotient genus:	$0$
Group name:	$C_9:D_4$
Group identifier:	$[72,8]$
Signature:	$[ 0; 2, 4, 18 ]$

Conjugacy classes for this refined passport:

$4, 6, 16$

Jacobian variety group algebra decomposition:	$E^{2}\times A_{3}^{2}$
Corresponding character(s):	$8, 10$

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) (37,46) (38,47) (39,48) (40,49) (41,50) (42,51) (43,52) (44,53) (45,54) (55,64) (56,65) (57,66) (58,67) (59,68) (60,69) (61,70) (62,71) (63,72)
Cyclic trigonal curve(s):	no

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

$y^2=x^{18}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.72-8.0.2-4-18.1.1

	(1,37) (2,39) (3,38) (4,44) (5,43) (6,45) (7,41) (8,40) (9,42) (10,46) (11,48) (12,47) (13,53) (14,52) (15,54) (16,50) (17,49) (18,51) (19,64) (20,66) (21,65) (22,71) (23,70) (24,72) (25,68) (26,67) (27,69) (28,55) (29,57) (30,56) (31,62) (32,61) (33,63) (34,59) (35,58) (36,60)
	(1,62,10,71) (2,61,11,70) (3,63,12,72) (4,59,13,68) (5,58,14,67) (6,60,15,69) (7,56,16,65) (8,55,17,64) (9,57,18,66) (19,53,28,44) (20,52,29,43) (21,54,30,45) (22,50,31,41) (23,49,32,40) (24,51,33,42) (25,47,34,38) (26,46,35,37) (27,48,36,39)
	(1,22,7,21,6,27,2,23,8,19,4,25,3,24,9,20,5,26) (10,31,16,30,15,36,11,32,17,28,13,34,12,33,18,29,14,35) (37,58,43,57,42,63,38,59,44,55,40,61,39,60,45,56,41,62) (46,67,52,66,51,72,47,68,53,64,49,70,48,69,54,65,50,71)