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

• Label: 8.72-8.0.2-4-18.5
• 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:

$4, 6, 20$

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.

8.72-8.0.2-4-18.5.1

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