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

• Label: 14.112-5.0.2-4-56.8
• 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:

$3, 5, 27$

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.

14.112-5.0.2-4-56.8.1

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