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

• Label: 14.120-30.0.2-4-30.7
• 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:

$4, 6, 32$

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.

14.120-30.0.2-4-30.7.1

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