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

• Label: 12.104-8.0.2-4-26.12
• 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:

$4, 5, 29$

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.

12.104-8.0.2-4-26.12.1

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