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

• Label: 13.112-13.0.2-4-28.10
• 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:

$5, 10, 28$

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.

13.112-13.0.2-4-28.10.1

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