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

• Label: 15.120-27.0.2-4-60.10
• 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:

$4, 8, 32$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$6, 11, 25, 29$

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.

15.120-27.0.2-4-60.10.1

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