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

• Label: 15.120-27.0.2-4-60.15
• 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:

$4, 9, 34$

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.

15.120-27.0.2-4-60.15.1

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