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

• Label: 13.104-5.0.2-4-52.2
• 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:

$3, 7, 24$

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

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.

13.104-5.0.2-4-52.2.1

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