Family Information
Genus: | $14$ |
Quotient genus: | $0$ |
Group name: | $C_5:C_4$ |
Group identifier: | $[20,1]$ |
Signature: | $[ 0; 2, 2, 4, 4, 5 ]$ |
Conjugacy classes for this refined passport: | $2, 2, 3, 4, 6$ |
Jacobian variety group algebra decomposition: | $A_{2}\times A_{12}$ |
Corresponding character(s): | $3, 5$ |
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: |
$y^2=(x^{10}-1)(x^{10}+a_{1}x^{5}+1)(x^{10}+a_{2}x^{5}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
14.20-1.0.2-2-4-4-5.2.1
(1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) | |
(1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) | |
(1,11,6,16) (2,15,7,20) (3,14,8,19) (4,13,9,18) (5,12,10,17) | |
(1,18,6,13) (2,17,7,12) (3,16,8,11) (4,20,9,15) (5,19,10,14) | |
(1,4,2,5,3) (6,9,7,10,8) (11,14,12,15,13) (16,19,17,20,18) |