One refined passport of genus 15 with automorphism group $C_4\times D_{15}$

• Label: 15.120-27.0.2-4-60.6
• Genus: \(15\)
• Quotient genus: \(0\)
• Group: \(C_4\times D_{15}\)
• Signature: \([ 0; 2, 4, 60 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$15$
Quotient genus:	$0$
Group name:	$C_4\times D_{15}$
Group identifier:	$[120,27]$
Signature:	$[ 0; 2, 4, 60 ]$

Conjugacy classes for this refined passport:

$3, 9, 32$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$5, 11, 25, 29$

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:

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.120-27.0.2-4-60.6.1

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