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

• Label: 15.120-27.0.2-4-60.4
• 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:

$3, 8, 36$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$5, 11, 25, 29$

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.

15.120-27.0.2-4-60.4.1

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