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

• Label: 15.128-147.0.2-4-32.8
• 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:

$5, 9, 38$

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.

15.128-147.0.2-4-32.8.1

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