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

• Label: 15.128-147.0.2-4-32.10
• 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:

$5, 10, 25$

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.

15.128-147.0.2-4-32.10.1

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