One refined passport of genus 15 with automorphism group $D_{16}:C_4$

• Label: 15.128-147.0.2-4-32.5
• Genus: \(15\)
• Quotient genus: \(0\)
• Group: \(D_{16}:C_4\)
• Signature: \([ 0; 2, 4, 32 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$15$
Quotient genus:	$0$
Group name:	$D_{16}:C_4$
Group identifier:	$[128,147]$
Signature:	$[ 0; 2, 4, 32 ]$

Conjugacy classes for this refined passport:

$5, 9, 32$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$6, 13, 16, 23$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,9) (2,10) (3,11) (4,12) (5,13) (6,14) (7,15) (8,16) (17,25) (18,26) (19,27) (20,28) (21,29) (22,30) (23,31) (24,32) (33,41) (34,42) (35,43) (36,44) (37,45) (38,46) (39,47) (40,48) (49,57) (50,58) (51,59) (52,60) (53,61) (54,62) (55,63) (56,64) (65,73) (66,74) (67,75) (68,76) (69,77) (70,78) (71,79) (72,80) (81,89) (82,90) (83,91) (84,92) (85,93) (86,94) (87,95) (88,96) (97,105) (98,106) (99,107) (100,108) (101,109) (102,110) (103,111) (104,112) (113,121) (114,122) (115,123) (116,124) (117,125) (118,126) (119,127) (120,128)
Cyclic trigonal curve(s):	no

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

$y^2=x^{32}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.128-147.0.2-4-32.5.1

	(1,33) (2,34) (3,36) (4,35) (5,39) (6,40) (7,37) (8,38) (9,41) (10,42) (11,44) (12,43) (13,47) (14,48) (15,45) (16,46) (17,53) (18,54) (19,56) (20,55) (21,49) (22,50) (23,52) (24,51) (25,61) (26,62) (27,64) (28,63) (29,57) (30,58) (31,60) (32,59) (65,97) (66,98) (67,100) (68,99) (69,103) (70,104) (71,101) (72,102) (73,105) (74,106) (75,108) (76,107) (77,111) (78,112) (79,109) (80,110) (81,117) (82,118) (83,120) (84,119) (85,113) (86,114) (87,116) (88,115) (89,125) (90,126) (91,128) (92,127) (93,121) (94,122) (95,124) (96,123)
	(1,70,9,78) (2,69,10,77) (3,71,11,79) (4,72,12,80) (5,66,13,74) (6,65,14,73) (7,67,15,75) (8,68,16,76) (17,83,25,91) (18,84,26,92) (19,81,27,89) (20,82,28,90) (21,86,29,94) (22,85,30,93) (23,87,31,95) (24,88,32,96) (33,118,41,126) (34,117,42,125) (35,119,43,127) (36,120,44,128) (37,114,45,122) (38,113,46,121) (39,115,47,123) (40,116,48,124) (49,102,57,110) (50,101,58,109) (51,103,59,111) (52,104,60,112) (53,98,61,106) (54,97,62,105) (55,99,63,107) (56,100,64,108)
	(1,112,31,116,6,105,26,119,4,110,29,114,7,108,27,117,2,111,32,115,5,106,25,120,3,109,30,113,8,107,28,118) (9,104,23,124,14,97,18,127,12,102,21,122,15,100,19,125,10,103,24,123,13,98,17,128,11,101,22,121,16,99,20,126) (33,90,63,68,38,93,58,71,36,91,61,66,39,96,59,69,34,89,64,67,37,94,57,72,35,92,62,65,40,95,60,70) (41,82,55,76,46,85,50,79,44,83,53,74,47,88,51,77,42,81,56,75,45,86,49,80,43,84,54,73,48,87,52,78)