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

• Label: 14.120-30.0.2-4-30.6
• 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:

$4, 6, 31$

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.

14.120-30.0.2-4-30.6.1

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