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

• Label: 15.120-27.0.2-4-60.1
• 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:

$3, 8, 30$

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.

15.120-27.0.2-4-60.1.1

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