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

• Label: 15.128-147.0.2-4-32.11
• 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:

$5, 10, 27$

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.

15.128-147.0.2-4-32.11.1

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