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

• Label: 14.112-5.0.2-4-56.9
• 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:

$3, 5, 28$

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.

14.112-5.0.2-4-56.9.1

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