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

• Label: 13.112-13.0.2-4-28.6
• 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:

$5, 9, 34$

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.

13.112-13.0.2-4-28.6.1

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