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

• Label: 11.96-28.0.2-4-24.15
• 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:

$6, 11, 29$

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.

11.96-28.0.2-4-24.15.1

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