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

• Label: 8.72-8.0.2-4-18.2
• 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:

$4, 6, 17$

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.

8.72-8.0.2-4-18.2.1

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