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

• Label: 14.112-5.0.2-4-56.5
• 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:

$3, 5, 24$

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.

14.112-5.0.2-4-56.5.1

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