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

• Label: 15.120-27.0.2-4-60.8
• 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:

$3, 9, 35$

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.

15.120-27.0.2-4-60.8.1

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