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

• Label: 13.104-5.0.2-4-52.22
• 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:

$4, 8, 29$

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.

13.104-5.0.2-4-52.22.1

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