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

• Label: 10.88-7.0.2-4-22.4
• 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:

$4, 5, 19$

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.

10.88-7.0.2-4-22.4.1

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