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

• Label: 15.120-27.0.2-4-60.9
• 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:

$4, 8, 29$

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.

15.120-27.0.2-4-60.9.1

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