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

• Label: 13.104-5.0.2-4-52.8
• 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:

$3, 8, 23$

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.

13.104-5.0.2-4-52.8.1

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