# Properties

 Genus $$12$$ Quotient genus $$0$$ Group $$SD_{32}$$ Signature $$[ 0; 2, 2, 4, 16 ]$$ Generating Vectors $$1$$

# Related objects

## Family Information

 Genus: 12 Quotient genus: 0 Group name: $SD_{32}$ Group identifier: [32,19] Signature: $[ 0; 2, 2, 4, 16 ]$
 Conjugacy classes for this refined passport: 2, 3, 5, 11

 Jacobian variety group algebra decomposition: $A_{6}^{2}$ Corresponding character(s): 8

## Other Data

 Hyperelliptic curve(s): Yes Hyperelliptic involution: (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) Cyclic trigonal curve(s): No

 Equation(s) of curve(s) in this refined passport:
 $y^2=x(x^{8}-1)(x^{16}+a_{1}x^{8}+1)$

## Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.32-19.0.2-2-4-16.4.1

 (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) (1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14) (17,25) (18,26) (19,28) (20,27) (21,31) (22,32) (23,29) (24,30) (1,19,2,20) (3,17,4,18) (5,22,6,21) (7,23,8,24) (9,31,10,32) (11,29,12,30) (13,27,14,28) (15,25,16,26) (1,28,7,29,3,25,6,31,2,27,8,30,4,26,5,32) (9,21,15,17,11,23,14,19,10,22,16,18,12,24,13,20)