# Properties

 Label 12.12-4.0.2-2-2-2-2-2-6.1 Genus $$12$$ Quotient genus $$0$$ Group $$D_6$$ Signature $$[ 0; 2, 2, 2, 2, 2, 2, 6 ]$$ Generating Vectors $$1$$

# Related objects

## Family Information

 Genus: $12$ Quotient genus: $0$ Group name: $D_6$ Group identifier: $[12,4]$ Signature: $[ 0; 2, 2, 2, 2, 2, 2, 6 ]$
 Conjugacy classes for this refined passport: $2, 2, 2, 2, 3, 4, 6$

 Jacobian variety group algebra decomposition: $A_{2}\times A_{2}\times A_{4}^{2}$ Corresponding character(s): $3, 4, 6$

## Other Data

 Hyperelliptic curve(s): yes Hyperelliptic involution: (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) Cyclic trigonal curve(s): no

 Equation(s) of curve(s) in this refined passport:
 $y^2=x(x^{6}+a_{1}x^{3}+1)(x^{6}+a_{2}x^{3}+1)(x^{6}+a_{3}x^{3}+1)(x^{6}+a_{4}x^{3}+1)$

## Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.12-4.0.2-2-2-2-2-2-6.1.1

 (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) (1,5,3,4,2,6) (7,11,9,10,8,12)