One refined passport of genus 13 with automorphism group $C_4\times D_{13}$

• Label: 13.104-5.0.2-4-52.14
• Genus: \(13\)
• Quotient genus: \(0\)
• Group: \(C_4\times D_{13}\)
• Signature: \([ 0; 2, 4, 52 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$13$
Quotient genus:	$0$
Group name:	$C_4\times D_{13}$
Group identifier:	$[104,5]$
Signature:	$[ 0; 2, 4, 52 ]$

Conjugacy classes for this refined passport:

$4, 7, 23$

Jacobian variety group algebra decomposition:	$E\times A_{6}^{2}$
Corresponding character(s):	$5, 21$

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:

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

13.104-5.0.2-4-52.14.1

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