One refined passport of genus 14 with automorphism group $C_{15}:D_4$

• Label: 14.120-30.0.2-4-30.8
• Genus: \(14\)
• Quotient genus: \(0\)
• Group: \(C_{15}:D_4\)
• Signature: \([ 0; 2, 4, 30 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$14$
Quotient genus:	$0$
Group name:	$C_{15}:D_4$
Group identifier:	$[120,30]$
Signature:	$[ 0; 2, 4, 30 ]$

Conjugacy classes for this refined passport:

$4, 6, 33$

Jacobian variety group algebra decomposition:	$E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$8, 10, 18$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,16) (2,17) (3,18) (4,19) (5,20) (6,21) (7,22) (8,23) (9,24) (10,25) (11,26) (12,27) (13,28) (14,29) (15,30) (31,46) (32,47) (33,48) (34,49) (35,50) (36,51) (37,52) (38,53) (39,54) (40,55) (41,56) (42,57) (43,58) (44,59) (45,60) (61,76) (62,77) (63,78) (64,79) (65,80) (66,81) (67,82) (68,83) (69,84) (70,85) (71,86) (72,87) (73,88) (74,89) (75,90) (91,106) (92,107) (93,108) (94,109) (95,110) (96,111) (97,112) (98,113) (99,114) (100,115) (101,116) (102,117) (103,118) (104,119) (105,120)
Cyclic trigonal curve(s):	no

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

$y^2=x^{30}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.120-30.0.2-4-30.8.1

	(1,61) (2,65) (3,64) (4,63) (5,62) (6,71) (7,75) (8,74) (9,73) (10,72) (11,66) (12,70) (13,69) (14,68) (15,67) (16,76) (17,80) (18,79) (19,78) (20,77) (21,86) (22,90) (23,89) (24,88) (25,87) (26,81) (27,85) (28,84) (29,83) (30,82) (31,106) (32,110) (33,109) (34,108) (35,107) (36,116) (37,120) (38,119) (39,118) (40,117) (41,111) (42,115) (43,114) (44,113) (45,112) (46,91) (47,95) (48,94) (49,93) (50,92) (51,101) (52,105) (53,104) (54,103) (55,102) (56,96) (57,100) (58,99) (59,98) (60,97)
	(1,97,16,112) (2,96,17,111) (3,100,18,115) (4,99,19,114) (5,98,20,113) (6,92,21,107) (7,91,22,106) (8,95,23,110) (9,94,24,109) (10,93,25,108) (11,102,26,117) (12,101,27,116) (13,105,28,120) (14,104,29,119) (15,103,30,118) (31,82,46,67) (32,81,47,66) (33,85,48,70) (34,84,49,69) (35,83,50,68) (36,77,51,62) (37,76,52,61) (38,80,53,65) (39,79,54,64) (40,78,55,63) (41,87,56,72) (42,86,57,71) (43,90,58,75) (44,89,59,74) (45,88,60,73)
	(1,45,9,33,12,36,5,44,8,32,11,40,4,43,7,31,15,39,3,42,6,35,14,38,2,41,10,34,13,37) (16,60,24,48,27,51,20,59,23,47,26,55,19,58,22,46,30,54,18,57,21,50,29,53,17,56,25,49,28,52) (61,105,69,93,72,96,65,104,68,92,71,100,64,103,67,91,75,99,63,102,66,95,74,98,62,101,70,94,73,97) (76,120,84,108,87,111,80,119,83,107,86,115,79,118,82,106,90,114,78,117,81,110,89,113,77,116,85,109,88,112)