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

• Label: 14.120-30.0.2-4-30.1
• 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:

$4, 6, 26$

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.

14.120-30.0.2-4-30.1.1

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