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

• Label: 15.120-27.0.2-4-60.7
• 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:

$3, 9, 33$

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.

15.120-27.0.2-4-60.7.1

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