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

• Label: 13.104-5.0.2-4-52.17
• 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:

$4, 7, 28$

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.

13.104-5.0.2-4-52.17.1

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