One refined passport of genus 14 with automorphism group $C_{56}:C_2$

• Label: 14.112-5.0.2-4-56.6
• Genus: \(14\)
• Quotient genus: \(0\)
• Group: \(C_{56}:C_2\)
• Signature: \([ 0; 2, 4, 56 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$14$
Quotient genus:	$0$
Group name:	$C_{56}:C_2$
Group identifier:	$[112,5]$
Signature:	$[ 0; 2, 4, 56 ]$

Conjugacy classes for this refined passport:

$3, 5, 25$

Jacobian variety group algebra decomposition:	$E^{2}\times A_{6}^{2}$
Corresponding character(s):	$12, 20$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14) (15,22) (16,23) (17,24) (18,25) (19,26) (20,27) (21,28) (29,36) (30,37) (31,38) (32,39) (33,40) (34,41) (35,42) (43,50) (44,51) (45,52) (46,53) (47,54) (48,55) (49,56) (57,64) (58,65) (59,66) (60,67) (61,68) (62,69) (63,70) (71,78) (72,79) (73,80) (74,81) (75,82) (76,83) (77,84) (85,92) (86,93) (87,94) (88,95) (89,96) (90,97) (91,98) (99,106) (100,107) (101,108) (102,109) (103,110) (104,111) (105,112)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x(x^{28}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.112-5.0.2-4-56.6.1

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