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

• Label: 11.96-28.0.2-4-24.3
• 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:

$5, 10, 29$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times E^{2}\times E^{2}\times A_{2}^{2}$
Corresponding character(s):	$6, 13, 15, 19, 24$

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.

11.96-28.0.2-4-24.3.1

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