Properties

Genus \(4\)
Small Group \(D_{10}\)
Signature \([ 0; 2, 2, 2, 5 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more about

Family Information

Genus: 4
Group name: $D_{10}$
Group identifier: [20,4]
Signature: $[ 0; 2, 2, 2, 5 ]$
Conjugacy classes for this refined passport: 2, 3, 4, 5

Jacobian variety group algebra decomposition:$A_{2}^{2}$
Corresponding character(s): 5

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{10}+a_1x^{5}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.20-4.0.2-2-2-5.1.1

  (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20)
  (1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
  (1,20) (2,19) (3,18) (4,17) (5,16) (6,15) (7,14) (8,13) (9,12) (10,11)
  (1,2,3,4,5) (6,7,8,9,10) (11,12,13,14,15) (16,17,18,19,20)