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

• Label: 15.120-27.0.2-4-60.3
• 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:

$3, 8, 34$

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.

15.120-27.0.2-4-60.3.1

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