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

• Label: 13.104-5.0.2-4-52.9
• 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:

$3, 8, 25$

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.

13.104-5.0.2-4-52.9.1

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