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

• Label: 10.88-7.0.2-4-22.3
• 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:

$4, 5, 18$

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.

10.88-7.0.2-4-22.3.1

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