Family Information
Genus: | $15$ |
Quotient genus: | $0$ |
Group name: | $D_{10}$ |
Group identifier: | $[20,4]$ |
Signature: | $[ 0; 2, 2, 2, 2, 2, 10 ]$ |
Conjugacy classes for this refined passport: | $2, 2, 2, 3, 3, 8$ |
Jacobian variety group algebra decomposition: | $A_{2}\times E\times A_{6}^{2}$ |
Corresponding character(s): | $3, 4, 5$ |
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: |
$y^2=x(x^{10}+a_{1}x^{5}+1)(x^{10}+a_{2}x^{5}+1)(x^{10}+a_{3}x^{5}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
15.20-4.0.2-2-2-2-2-10.2.1
(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) | |
(1,6) (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) | |
(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19) | |
(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18) |