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

• Label: 13.104-5.0.2-4-52.19
• 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:

$4, 8, 22$

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.

13.104-5.0.2-4-52.19.1

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