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

• Label: 13.112-13.0.2-4-28.12
• 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:

$5, 10, 33$

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.

13.112-13.0.2-4-28.12.1

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