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

• Label: 11.96-28.0.2-4-24.7
• 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:

$5, 11, 27$

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.

11.96-28.0.2-4-24.7.1

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