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

• Label: 13.104-5.0.2-4-52.21
• 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:

$4, 8, 26$

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.

13.104-5.0.2-4-52.21.1

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