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

• Label: 13.104-5.0.2-4-52.3
• 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:

$3, 7, 26$

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.

13.104-5.0.2-4-52.3.1

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