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

• Label: 13.104-5.0.2-4-52.5
• 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:

$3, 7, 31$

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.

13.104-5.0.2-4-52.5.1

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