Properties

Genus \(7\)
Quotient Genus \(0\)
Group \(C_2^2.D_8\)
Signature \([ 0; 2, 4, 16 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more about

Family Information

Genus: 7
Quotient Genus: 0
Group name: $C_2^2.D_8$
Group identifier: [64,38]
Signature: $[ 0; 2, 4, 16 ]$
Conjugacy classes for this refined passport: 5, 9, 18

Jacobian variety group algebra decomposition:$E\times E^{2}\times A_{2}^{2}$
Corresponding character(s): 6, 12, 17

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,5) (2,6) (3,7) (4,8) (9,13) (10,14) (11,15) (12,16) (17,21) (18,22) (19,23) (20,24) (25,29) (26,30) (27,31) (28,32) (33,37) (34,38) (35,39) (36,40) (41,45) (42,46) (43,47) (44,48) (49,53) (50,54) (51,55) (52,56) (57,61) (58,62) (59,63) (60,64)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{16}-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

7.64-38.0.2-4-16.2.1

  (1,17) (2,18) (3,20) (4,19) (5,21) (6,22) (7,24) (8,23) (9,27) (10,28) (11,25) (12,26) (13,31) (14,32) (15,29) (16,30) (33,49) (34,50) (35,52) (36,51) (37,53) (38,54) (39,56) (40,55) (41,59) (42,60) (43,57) (44,58) (45,63) (46,64) (47,61) (48,62)
  (1,34,5,38) (2,33,6,37) (3,35,7,39) (4,36,8,40) (9,44,13,48) (10,43,14,47) (11,42,15,46) (12,41,16,45) (17,58,21,62) (18,57,22,61) (19,59,23,63) (20,60,24,64) (25,50,29,54) (26,49,30,53) (27,51,31,55) (28,52,32,56)
  (1,54,15,60,3,56,14,57,2,53,16,59,4,55,13,58) (5,50,11,64,7,52,10,61,6,49,12,63,8,51,9,62) (17,48,31,36,19,45,30,33,18,47,32,35,20,46,29,34) (21,44,27,40,23,41,26,37,22,43,28,39,24,42,25,38)