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

• Label: 13.104-5.0.2-4-52.6
• 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:

$3, 7, 32$

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.

13.104-5.0.2-4-52.6.1

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