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

• Label: 15.120-27.0.2-4-60.12
• 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:

$4, 8, 35$

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.

15.120-27.0.2-4-60.12.1

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