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

• Label: 8.72-8.0.2-4-18.4
• 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:

$4, 6, 19$

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.

8.72-8.0.2-4-18.4.1

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