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

• Label: 15.128-147.0.2-4-32.14
• 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:

$5, 10, 33$

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.

15.128-147.0.2-4-32.14.1

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