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

• Label: 12.104-8.0.2-4-26.10
• 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:

$4, 5, 27$

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.

12.104-8.0.2-4-26.10.1

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