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

• Label: 13.104-5.0.2-4-52.10
• 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:

$3, 8, 27$

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.

13.104-5.0.2-4-52.10.1

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