One refined passport of genus 12 with automorphism group $C_{13}:D_4$

• Label: 12.104-8.0.2-4-26.8
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(C_{13}:D_4\)
• Signature: \([ 0; 2, 4, 26 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$C_{13}:D_4$
Group identifier:	$[104,8]$
Signature:	$[ 0; 2, 4, 26 ]$

Conjugacy classes for this refined passport:

$4, 5, 25$

Jacobian variety group algebra decomposition:	$A_{6}^{2}$
Corresponding character(s):	$6$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,14) (2,15) (3,16) (4,17) (5,18) (6,19) (7,20) (8,21) (9,22) (10,23) (11,24) (12,25) (13,26) (27,40) (28,41) (29,42) (30,43) (31,44) (32,45) (33,46) (34,47) (35,48) (36,49) (37,50) (38,51) (39,52) (53,66) (54,67) (55,68) (56,69) (57,70) (58,71) (59,72) (60,73) (61,74) (62,75) (63,76) (64,77) (65,78) (79,92) (80,93) (81,94) (82,95) (83,96) (84,97) (85,98) (86,99) (87,100) (88,101) (89,102) (90,103) (91,104)
Cyclic trigonal curve(s):	no

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

$y^2=x^{26}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.104-8.0.2-4-26.8.1

	(1,53) (2,65) (3,64) (4,63) (5,62) (6,61) (7,60) (8,59) (9,58) (10,57) (11,56) (12,55) (13,54) (14,66) (15,78) (16,77) (17,76) (18,75) (19,74) (20,73) (21,72) (22,71) (23,70) (24,69) (25,68) (26,67) (27,92) (28,104) (29,103) (30,102) (31,101) (32,100) (33,99) (34,98) (35,97) (36,96) (37,95) (38,94) (39,93) (40,79) (41,91) (42,90) (43,89) (44,88) (45,87) (46,86) (47,85) (48,84) (49,83) (50,82) (51,81) (52,80)
	(1,88,14,101) (2,87,15,100) (3,86,16,99) (4,85,17,98) (5,84,18,97) (6,83,19,96) (7,82,20,95) (8,81,21,94) (9,80,22,93) (10,79,23,92) (11,91,24,104) (12,90,25,103) (13,89,26,102) (27,75,40,62) (28,74,41,61) (29,73,42,60) (30,72,43,59) (31,71,44,58) (32,70,45,57) (33,69,46,56) (34,68,47,55) (35,67,48,54) (36,66,49,53) (37,78,50,65) (38,77,51,64) (39,76,52,63)
	(1,31,9,39,4,34,12,29,7,37,2,32,10,27,5,35,13,30,8,38,3,33,11,28,6,36) (14,44,22,52,17,47,25,42,20,50,15,45,23,40,18,48,26,43,21,51,16,46,24,41,19,49) (53,83,61,91,56,86,64,81,59,89,54,84,62,79,57,87,65,82,60,90,55,85,63,80,58,88) (66,96,74,104,69,99,77,94,72,102,67,97,75,92,70,100,78,95,73,103,68,98,76,93,71,101)