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

• Label: 13.104-5.0.2-4-52.13
• 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:

$4, 7, 21$

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.

13.104-5.0.2-4-52.13.1

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