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

• Label: 13.112-13.0.2-4-28.3
• 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:

$5, 9, 29$

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.

13.112-13.0.2-4-28.3.1

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