# Properties

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

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## 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, 10

 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.

12.32-19.0.2-2-4-16.3.1

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