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

• Label: 8.72-8.0.2-4-18.6
• 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:

$4, 6, 21$

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.

8.72-8.0.2-4-18.6.1

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