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

• Label: 13.112-13.0.2-4-28.11
• 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:

$5, 10, 30$

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.

13.112-13.0.2-4-28.11.1

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