One refined passport of genus 13 with automorphism group $D_{14}:C_4$

• Label: 13.112-13.0.2-4-28.2
• Genus: \(13\)
• Quotient genus: \(0\)
• Group: \(D_{14}:C_4\)
• Signature: \([ 0; 2, 4, 28 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$13$
Quotient genus:	$0$
Group name:	$D_{14}:C_4$
Group identifier:	$[112,13]$
Signature:	$[ 0; 2, 4, 28 ]$

Conjugacy classes for this refined passport:

$5, 9, 27$

Jacobian variety group algebra decomposition:	$E\times A_{3}^{2}\times A_{3}^{2}$
Corresponding character(s):	$5, 11, 25$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,22) (2,23) (3,24) (4,25) (5,26) (6,27) (7,28) (8,15) (9,16) (10,17) (11,18) (12,19) (13,20) (14,21) (29,50) (30,51) (31,52) (32,53) (33,54) (34,55) (35,56) (36,43) (37,44) (38,45) (39,46) (40,47) (41,48) (42,49) (57,78) (58,79) (59,80) (60,81) (61,82) (62,83) (63,84) (64,71) (65,72) (66,73) (67,74) (68,75) (69,76) (70,77) (85,106) (86,107) (87,108) (88,109) (89,110) (90,111) (91,112) (92,99) (93,100) (94,101) (95,102) (96,103) (97,104) (98,105)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x^{28}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

13.112-13.0.2-4-28.2.1

	(1,57) (2,63) (3,62) (4,61) (5,60) (6,59) (7,58) (8,64) (9,70) (10,69) (11,68) (12,67) (13,66) (14,65) (15,71) (16,77) (17,76) (18,75) (19,74) (20,73) (21,72) (22,78) (23,84) (24,83) (25,82) (26,81) (27,80) (28,79) (29,92) (30,98) (31,97) (32,96) (33,95) (34,94) (35,93) (36,85) (37,91) (38,90) (39,89) (40,88) (41,87) (42,86) (43,106) (44,112) (45,111) (46,110) (47,109) (48,108) (49,107) (50,99) (51,105) (52,104) (53,103) (54,102) (55,101) (56,100)
	(1,88,22,109) (2,87,23,108) (3,86,24,107) (4,85,25,106) (5,91,26,112) (6,90,27,111) (7,89,28,110) (8,95,15,102) (9,94,16,101) (10,93,17,100) (11,92,18,99) (12,98,19,105) (13,97,20,104) (14,96,21,103) (29,81,50,60) (30,80,51,59) (31,79,52,58) (32,78,53,57) (33,84,54,63) (34,83,55,62) (35,82,56,61) (36,74,43,67) (37,73,44,66) (38,72,45,65) (39,71,46,64) (40,77,47,70) (41,76,48,69) (42,75,49,68)
	(1,47,16,34,3,49,18,29,5,44,20,31,7,46,15,33,2,48,17,35,4,43,19,30,6,45,21,32) (8,54,23,41,10,56,25,36,12,51,27,38,14,53,22,40,9,55,24,42,11,50,26,37,13,52,28,39) (57,103,72,90,59,105,74,85,61,100,76,87,63,102,71,89,58,104,73,91,60,99,75,86,62,101,77,88) (64,110,79,97,66,112,81,92,68,107,83,94,70,109,78,96,65,111,80,98,67,106,82,93,69,108,84,95)