Generated 8/31/05 2-cocycle twisted invariants Z_5[t,t^(-1)]/(t^2+1) 4 element quandles [0 2 1 0] [ ] [2 1 0 1] [ ] [1 0 2 2] [ ] [3 3 3 3] Knot, 1 [[10, 0]] Knot, 2 [[4, 0]] Knot, 3 [[4, 0]] Knot, 4 [[4, 0]] Knot, 5 [[4, 0], [1, (4 x[5] + 3 x[1] + x[3] + 2 x[4] + 2 x[2]) t + 4 x[2] + 2 x[5] + 2 x[3] + 4 x[4] + 2 x[1]], [1, (4 x[5] + 2 x[4] + 3 x[3] + 3 x[1]) t + 2 x[2] + 2 x[5] + x[1] + 3 x[4]], [1, (3 x[5] + 4 x[1] + 2 x[3] + x[4] + 2 x[2]) t + 4 x[2] + 2 x[1] + 4 x[3] + 2 x[4] + 2 x[5]], [1, (4 x[1] + 2 x[3] + 3 x[4] + 3 x[5]) t + 2 x[2] + x[5] + 2 x[1] + 3 x[3]], [1, (3 x[1] + 2 x[3] + 3 x[2] + 3 x[5]) t + 2 x[5] + x[1] + x[4] + 4 x[2]] , [1, (3 x[5] + 2 x[4] + 3 x[2] + 3 x[1]) t + 2 x[1] + x[5] + x[3] + 4 x[2]] ] Knot, 6 [[4, 0]] Knot, 7 [[4, 0]] Knot, 8 [[4, 0]] Knot, 9 [[4, 0]] Knot, 10 [[4, 0]] Knot, 11 [[4, 0], [2, (4 x[4] + 4 x[1] + 3 x[2] + 3 x[3] + 3 x[5]) t + 4 x[3] + x[4] + 3 x[5] + 4 x[1]], [2, (3 x[5] + 3 x[4] + 3 x[3] + 3 x[1] + 4 x[2]) t + 3 x[5] + 3 x[1]], [2, (3 x[4] + 3 x[1] + 3 x[2] + 4 x[3] + 4 x[5]) t + x[3] + 4 x[4] + 4 x[5] + 3 x[1]]] Knot, 12 [[4, 0]] Knot, 13 [[4, 0]] Knot, 14 [[4, 0], [2, (4 x[4] + 2 x[3] + 4 x[2]) t + 3 x[5] + 4 x[2] + 4 x[1] + x[3]], [2, (4 x[3] + 2 x[4] + 4 x[2]) t + 3 x[1] + 4 x[2] + 4 x[5] + x[4]], [ 2, (4 x[3] + 4 x[4] + 2 x[2]) t + 3 x[5] + 2 x[2] + 4 x[4] + 4 x[3] + 3 x[1]]] Knot, 15 [[4, 0]] Knot, 16 [[4, 0]] Knot, 17 [[4, 0]] Knot, 18 [[4, 0]] Knot, 19 [[10, 0]] Knot, 20 [[4, 0]] Knot, 21 [[4, 0]] Knot, 22 [[4, 0]] Knot, 23 [[4, 0]] Knot, 24 [[10, 0]] Knot, 25 [[4, 0], [2, (3 x[5] + 3 x[3] + 3 x[4] + 4 x[2] + 3 x[1]) t + 3 x[5] + 3 x[1]], [2, (3 x[1] + 4 x[3] + 3 x[4] + 3 x[2] + 4 x[5]) t + 4 x[4] + 4 x[5] + x[3] + 3 x[1]], [2, (3 x[5] + 3 x[3] + 4 x[4] + 3 x[2] + 4 x[1]) t + x[4] + 4 x[1] + 4 x[3] + 3 x[5]]] Knot, 26 [[4, 0]] Knot, 27 [[4, 0]] Knot, 28 [[4, 0]] Knot, 29 [[10, 0]] Knot, 30 [[4, 0]] Knot, 31 [[4, 0]] Knot, 32 [[4, 0], [4, (3 x[5] + x[3] + 4 x[1] + 4 x[2]) t + 3 x[3] + x[4] + x[2]], [4, (3 x[1] + x[4] + 4 x[5] + 4 x[2]) t + x[3] + 3 x[4] + x[2]], [4, (3 x[5] + 3 x[1] + 4 x[3] + 4 x[4] + 2 x[2]) t + x[4] + 3 x[2] + x[3]] , [4, (x[5] + 4 x[4] + 2 x[1] + x[2]) t + 4 x[2] + 4 x[3] + 2 x[4]], [ 4, (2 x[5] + x[3] + x[4] + 3 x[2] + 2 x[1]) t + 4 x[3] + 2 x[2] + 4 x[4]] , [4, (2 x[5] + 4 x[3] + x[1] + x[2]) t + 4 x[2] + 2 x[3] + 4 x[4]]] Knot, 33 [[10, 0]] Knot, 34 [[10, 0]] Knot, 35 [[10, 0]] [0 0 1 1] [ ] [1 1 0 0] [ ] [3 3 2 2] [ ] [2 2 3 3] Knot, 1 [[4, 0]] Knot, 2 [[4, 0]] Knot, 3 [[4, 0]] Knot, 4 [[4, 0]] Knot, 5 [[4, 0]] Knot, 6 [[4, 0]] Knot, 7 [[4, 0]] Knot, 8 [[4, 0]] Knot, 9 [[4, 0]] Knot, 10 [[4, 0]] Knot, 11 [[4, 0]] Knot, 12 [[4, 0]] Knot, 13 [[4, 0]] Knot, 14 [[4, 0]] Knot, 15 [[4, 0]] Knot, 16 [[4, 0]] Knot, 17 [[4, 0]] Knot, 18 [[4, 0]] Knot, 19 [[4, 0]] Knot, 20 [[4, 0]] Knot, 21 [[4, 0]] Knot, 22 [[4, 0]] Knot, 23 [[4, 0]] Knot, 24 [[4, 0]] Knot, 25 [[4, 0]] Knot, 26 [[4, 0]] Knot, 27 [[4, 0]] Knot, 28 [[4, 0]] Knot, 29 [[4, 0]] Knot, 30 [[4, 0]] Knot, 31 [[4, 0]] Knot, 32 [[4, 0]] Knot, 33 [[4, 0]] Knot, 34 [[4, 0]] Knot, 35 [[4, 0]] [0 3 1 2] [ ] [2 1 3 0] [ ] [3 0 2 1] [ ] [1 2 0 3] Knot, 1 [[16, 0]] Knot, 2 [[4, 0], [2, (2 x[1] + 3 x[2] + 3 x[4] + 4 x[3] + 4 x[6]) t + x[3] + x[6]], [2, (4 x[2] + x[4] + 4 x[5] + x[6]) t + 4 x[6] + 4 x[4] + 4 x[5] + 4 x[2]] , [2, (x[3] + x[4] + x[1] + 4 x[5] + 4 x[6]) t + x[5] + 4 x[1] + x[3] + x[4] + x[6]], [2, (4 x[4] + x[5] + x[2] + 4 x[6]) t + x[6] + x[2] + x[4] + x[5]], [2, (3 x[1] + 2 x[4] + 2 x[2] + x[3] + x[6]) t + 4 x[3] + 4 x[6]], [2, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[6]) t + 4 x[5] + x[1] + 4 x[3] + 4 x[4] + 4 x[6]]] Knot, 3 [[4, 0]] Knot, 4 [[4, 0]] Knot, 5 [[4, 0]] Knot, 6 [[4, 0]] Knot, 7 [[4, 0]] Knot, 8 [[4, 0]] Knot, 9 [[4, 0], [2, (4 x[2] + x[4] + 4 x[5] + x[6]) t + 4 x[2] + 4 x[4] + 4 x[5] + 4 x[6]] , [2, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[6]) t + x[1] + 4 x[3] + 4 x[4] + 4 x[5] + 4 x[6]], [2, (2 x[1] + 3 x[2] + 4 x[3] + 3 x[4] + 4 x[6]) t + x[3] + x[6]], [2, (x[2] + 4 x[4] + x[5] + 4 x[6]) t + x[4] + x[5] + x[2] + x[6]], [ 2, (x[1] + x[3] + x[4] + 4 x[5] + 4 x[6]) t + x[3] + x[4] + 4 x[1] + x[5] + x[6]], [2, (3 x[1] + 2 x[2] + x[3] + 2 x[4] + x[6]) t + 4 x[3] + 4 x[6]]] Knot, 10 [[4, 0], [2, (4 x[2] + x[4] + 4 x[5] + x[6]) t + 4 x[2] + 4 x[4] + 4 x[5] + 4 x[6]] , [2, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[6]) t + x[1] + 4 x[3] + 4 x[4] + 4 x[5] + 4 x[6]], [2, (2 x[1] + 3 x[2] + 4 x[3] + 3 x[4] + 4 x[6]) t + x[3] + x[6]], [2, (x[2] + 4 x[4] + x[5] + 4 x[6]) t + x[4] + x[5] + x[2] + x[6]], [ 2, (x[1] + x[3] + x[4] + 4 x[5] + 4 x[6]) t + x[3] + x[4] + 4 x[1] + x[5] + x[6]], [2, (3 x[1] + 2 x[2] + x[3] + 2 x[4] + x[6]) t + 4 x[3] + 4 x[6]]] Knot, 11 [[4, 0]] Knot, 12 [[4, 0]] Knot, 13 [[4, 0]] Knot, 14 [[4, 0]] Knot, 15 [[16, 0]] Knot, 16 [[4, 0]] Knot, 17 [[4, 0]] Knot, 18 [[4, 0], [2, (x[1] + 4 x[3] + 4 x[4] + 4 x[5] + 4 x[6]) t + x[1] + x[3] + 4 x[6] + x[4] + 4 x[5]], [2, (4 x[2] + 4 x[4] + 4 x[5] + 4 x[6]) t + 4 x[4] + x[5] + x[2] + 4 x[6]] , [2, (x[2] + x[4] + x[5] + x[6]) t + 4 x[2] + x[4] + 4 x[5] + x[6]], [2, (x[3] + x[6]) t + 3 x[1] + x[3] + 2 x[4] + x[6] + 2 x[2]], [2, (4 x[1] + x[3] + x[4] + x[5] + x[6]) t + 4 x[3] + 4 x[4] + 4 x[1] + x[5] + x[6]], [2, (4 x[3] + 4 x[6]) t + 3 x[2] + 4 x[3] + 3 x[4] + 2 x[1] + 4 x[6]]] Knot, 19 [[16, 0]] Knot, 20 [[4, 0]] Knot, 21 [[4, 0]] Knot, 22 [[4, 0]] Knot, 23 [[4, 0]] Knot, 24 [[16, 0]] Knot, 25 [[4, 0], [2, (3 x[2] + 3 x[3] + 3 x[4] + 2 x[1] + 3 x[6]) t + 3 x[4] + 3 x[2] + 2 x[1]], [2, (2 x[1] + 3 x[5] + 3 x[6]) t + 2 x[4] + 2 x[3]], [2, (3 x[1] + 2 x[3] + 2 x[4] + 2 x[6] + 2 x[2]) t + 3 x[1] + 2 x[4] + 2 x[2]], [2, (3 x[4] + 3 x[6]) t + 2 x[5] + 2 x[2]], [2, (3 x[1] + 2 x[5] + 2 x[6]) t + 3 x[4] + 3 x[3]], [2, (2 x[4] + 2 x[6]) t + 3 x[5] + 3 x[2]]] Knot, 26 [[4, 0]] Knot, 27 [[4, 0], [2, (x[2] + 4 x[4] + x[5] + 4 x[6]) t + x[2] + x[6] + x[4] + x[5]], [2, (4 x[2] + x[4] + 4 x[5] + x[6]) t + 4 x[5] + 4 x[6] + 4 x[2] + 4 x[4]] , [2, (2 x[1] + 3 x[2] + 4 x[3] + 3 x[4] + 4 x[6]) t + x[3] + x[6]], [ 2, (x[1] + x[3] + x[4] + 4 x[5] + 4 x[6]) t + 4 x[1] + x[5] + x[3] + x[4] + x[6]], [2, (3 x[1] + 2 x[2] + x[3] + 2 x[4] + x[6]) t + 4 x[3] + 4 x[6]], [2, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[6]) t + 4 x[4] + 4 x[5] + x[1] + 4 x[3] + 4 x[6]]] Knot, 28 [[4, 0]] Knot, 29 [[16, 0]] Knot, 30 [[4, 0]] Knot, 31 [[4, 0]] Knot, 32 [[4, 0], [2, (2 x[3] + 2 x[4] + 2 x[1] + 3 x[5] + 3 x[6]) t + 2 x[5] + 2 x[6] + 2 x[4] + 2 x[3] + 3 x[1]], [8, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[6]) t + 4 x[5] + 4 x[6] + 4 x[4] + 4 x[3] + x[1]], [2, (3 x[2] + 2 x[4] + 3 x[5] + 2 x[6]) t + 3 x[5] + 3 x[2] + 3 x[6] + 3 x[4]], [2, (2 x[2] + 3 x[4] + 2 x[5] + 3 x[6]) t + 2 x[6] + 2 x[2] + 2 x[4] + 2 x[5]], [8, (3 x[2] + 4 x[3] + 3 x[4] + 2 x[1] + 4 x[6]) t + x[3] + x[6]], [2, (3 x[1] + 3 x[3] + 3 x[4] + 2 x[5] + 2 x[6]) t + 2 x[1] + 3 x[4] + 3 x[3] + 3 x[6] + 3 x[5]], [8, (x[1] + x[4] + 4 x[5] + x[3] + 4 x[6]) t + x[5] + 4 x[1] + x[3] + x[4] + x[6]], [8, (x[2] + 4 x[4] + x[5] + 4 x[6]) t + x[6] + x[2] + x[4] + x[5]], [ 8, (4 x[2] + x[4] + 4 x[5] + x[6]) t + 4 x[5] + 4 x[2] + 4 x[4] + 4 x[6]] , [2, (4 x[2] + 2 x[3] + 4 x[4] + x[1] + 2 x[6]) t + 3 x[3] + 3 x[6]], [2, (4 x[1] + x[2] + x[4] + 3 x[3] + 3 x[6]) t + 2 x[3] + 2 x[6]], [8, (2 x[2] + x[3] + 2 x[4] + 3 x[1] + x[6]) t + 4 x[3] + 4 x[6]]] Knot, 33 [[16, 0]] Knot, 34 [[16, 0]] Knot, 35 [[16, 0]]