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

• Label: 13.104-5.0.2-4-52.15
• 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:

$4, 7, 25$

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.

13.104-5.0.2-4-52.15.1

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