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

• Label: 15.120-27.0.2-4-60.11
• 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:

$4, 8, 33$

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.

15.120-27.0.2-4-60.11.1

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