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

• Label: 15.120-35.0.2-6-10.2
• 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:

$4, 8, 10$

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.

15.120-35.0.2-6-10.2.1

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