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

• Label: 15.120-27.0.2-4-60.5
• 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:

$3, 9, 29$

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.

15.120-27.0.2-4-60.5.1

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