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

• Label: 15.128-147.0.2-4-32.6
• 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:

$5, 9, 34$

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.

15.128-147.0.2-4-32.6.1

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