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

• Label: 13.112-13.0.2-4-28.16
• 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:

$6, 9, 28$

Jacobian variety group algebra decomposition:	$E\times A_{3}^{2}\times A_{3}^{2}$
Corresponding character(s):	$6, 11, 25$

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.

13.112-13.0.2-4-28.16.1

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