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

• Label: 13.112-13.0.2-4-28.8
• 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:

$5, 10, 25$

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.

13.112-13.0.2-4-28.8.1

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