One refined passport of genus 10 with automorphism group $C_{11}:D_4$

• Label: 10.88-7.0.2-4-22.8
• Genus: \(10\)
• Quotient genus: \(0\)
• Group: \(C_{11}:D_4\)
• Signature: \([ 0; 2, 4, 22 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$10$
Quotient genus:	$0$
Group name:	$C_{11}:D_4$
Group identifier:	$[88,7]$
Signature:	$[ 0; 2, 4, 22 ]$

Conjugacy classes for this refined passport:

$4, 5, 23$

Jacobian variety group algebra decomposition:	$A_{5}^{2}$
Corresponding character(s):	$6$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,12) (2,13) (3,14) (4,15) (5,16) (6,17) (7,18) (8,19) (9,20) (10,21) (11,22) (23,34) (24,35) (25,36) (26,37) (27,38) (28,39) (29,40) (30,41) (31,42) (32,43) (33,44) (45,56) (46,57) (47,58) (48,59) (49,60) (50,61) (51,62) (52,63) (53,64) (54,65) (55,66) (67,78) (68,79) (69,80) (70,81) (71,82) (72,83) (73,84) (74,85) (75,86) (76,87) (77,88)
Cyclic trigonal curve(s):	no

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

$y^2=x^{22}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.88-7.0.2-4-22.8.1

	(1,45) (2,55) (3,54) (4,53) (5,52) (6,51) (7,50) (8,49) (9,48) (10,47) (11,46) (12,56) (13,66) (14,65) (15,64) (16,63) (17,62) (18,61) (19,60) (20,59) (21,58) (22,57) (23,78) (24,88) (25,87) (26,86) (27,85) (28,84) (29,83) (30,82) (31,81) (32,80) (33,79) (34,67) (35,77) (36,76) (37,75) (38,74) (39,73) (40,72) (41,71) (42,70) (43,69) (44,68)
	(1,72,12,83) (2,71,13,82) (3,70,14,81) (4,69,15,80) (5,68,16,79) (6,67,17,78) (7,77,18,88) (8,76,19,87) (9,75,20,86) (10,74,21,85) (11,73,22,84) (23,61,34,50) (24,60,35,49) (25,59,36,48) (26,58,37,47) (27,57,38,46) (28,56,39,45) (29,66,40,55) (30,65,41,54) (31,64,42,53) (32,63,43,52) (33,62,44,51)
	(1,29,2,30,3,31,4,32,5,33,6,23,7,24,8,25,9,26,10,27,11,28) (12,40,13,41,14,42,15,43,16,44,17,34,18,35,19,36,20,37,21,38,22,39) (45,73,46,74,47,75,48,76,49,77,50,67,51,68,52,69,53,70,54,71,55,72) (56,84,57,85,58,86,59,87,60,88,61,78,62,79,63,80,64,81,65,82,66,83)