One refined passport of genus 15 with automorphism group $C_2\times A_5$

• Label: 15.120-35.0.2-6-10.1
• Genus: \(15\)
• Quotient genus: \(0\)
• Group: \(C_2\times A_5\)
• Signature: \([ 0; 2, 6, 10 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$15$
Quotient genus:	$0$
Group name:	$C_2\times A_5$
Group identifier:	$[120,35]$
Signature:	$[ 0; 2, 6, 10 ]$

Conjugacy classes for this refined passport:

$4, 8, 9$

Jacobian variety group algebra decomposition:	$A_{2}^{3}\times E^{4}\times E^{5}$
Corresponding character(s):	$5, 8, 10$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,61) (2,62) (3,63) (4,64) (5,65) (6,66) (7,67) (8,68) (9,69) (10,70) (11,71) (12,72) (13,73) (14,74) (15,75) (16,76) (17,77) (18,78) (19,79) (20,80) (21,81) (22,82) (23,83) (24,84) (25,85) (26,86) (27,87) (28,88) (29,89) (30,90) (31,91) (32,92) (33,93) (34,94) (35,95) (36,96) (37,97) (38,98) (39,99) (40,100) (41,101) (42,102) (43,103) (44,104) (45,105) (46,106) (47,107) (48,108) (49,109) (50,110) (51,111) (52,112) (53,113) (54,114) (55,115) (56,116) (57,117) (58,118) (59,119) (60,120)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x(x^{10}+11x^5-1)(x^{20}-228x^{15}+494x^{10}+228x^5+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.120-35.0.2-6-10.1.1

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