# Properties

 Genus $$8$$ Quotient genus $$0$$ Group $$D_{16}$$ Signature $$[ 0; 2, 2, 2, 16 ]$$ Generating Vectors $$1$$

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## Family Information

 Genus: 8 Quotient genus: 0 Group name: $D_{16}$ Group identifier: [32,18] Signature: $[ 0; 2, 2, 2, 16 ]$
 Conjugacy classes for this refined passport: 2, 3, 4, 10

 Jacobian variety group algebra decomposition: $A_{4}^{2}$ 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:
 $y^2=x(x^{16}+a_{1}x^{8}+1)$

## Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.32-18.0.2-2-2-16.3.1

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