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

• Label: 11.96-28.0.2-4-24.13
• 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:

$6, 11, 25$

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.

11.96-28.0.2-4-24.13.1

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