One refined passport of genus 11 with automorphism group $D_{12}:C_4$

• Label: 11.96-28.0.2-4-24.10
• Genus: \(11\)
• Quotient genus: \(0\)
• Group: \(D_{12}:C_4\)
• Signature: \([ 0; 2, 4, 24 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$11$
Quotient genus:	$0$
Group name:	$D_{12}:C_4$
Group identifier:	$[96,28]$
Signature:	$[ 0; 2, 4, 24 ]$

Conjugacy classes for this refined passport:

$6, 10, 24$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times E^{2}\times E^{2}\times A_{2}^{2}$
Corresponding character(s):	$5, 13, 15, 19, 24$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,10) (2,11) (3,12) (4,7) (5,8) (6,9) (13,22) (14,23) (15,24) (16,19) (17,20) (18,21) (25,34) (26,35) (27,36) (28,31) (29,32) (30,33) (37,46) (38,47) (39,48) (40,43) (41,44) (42,45) (49,58) (50,59) (51,60) (52,55) (53,56) (54,57) (61,70) (62,71) (63,72) (64,67) (65,68) (66,69) (73,82) (74,83) (75,84) (76,79) (77,80) (78,81) (85,94) (86,95) (87,96) (88,91) (89,92) (90,93)
Cyclic trigonal curve(s):	no

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

$y^2=x^{24}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

11.96-28.0.2-4-24.10.1

	(1,55) (2,57) (3,56) (4,58) (5,60) (6,59) (7,49) (8,51) (9,50) (10,52) (11,54) (12,53) (13,70) (14,72) (15,71) (16,67) (17,69) (18,68) (19,64) (20,66) (21,65) (22,61) (23,63) (24,62) (25,91) (26,93) (27,92) (28,94) (29,96) (30,95) (31,85) (32,87) (33,86) (34,88) (35,90) (36,89) (37,79) (38,81) (39,80) (40,82) (41,84) (42,83) (43,73) (44,75) (45,74) (46,76) (47,78) (48,77)
	(1,75,10,84) (2,74,11,83) (3,73,12,82) (4,78,7,81) (5,77,8,80) (6,76,9,79) (13,90,22,93) (14,89,23,92) (15,88,24,91) (16,87,19,96) (17,86,20,95) (18,85,21,94) (25,60,34,51) (26,59,35,50) (27,58,36,49) (28,57,31,54) (29,56,32,53) (30,55,33,52) (37,69,46,66) (38,68,47,65) (39,67,48,64) (40,72,43,63) (41,71,44,62) (42,70,45,61)
	(1,41,24,34,5,39,19,32,3,40,23,36,4,38,21,31,2,42,22,35,6,37,20,33) (7,47,18,28,11,45,13,26,9,46,17,30,10,44,15,25,8,48,16,29,12,43,14,27) (49,89,72,82,53,87,67,80,51,88,71,84,52,86,69,79,50,90,70,83,54,85,68,81) (55,95,66,76,59,93,61,74,57,94,65,78,58,92,63,73,56,96,64,77,60,91,62,75)