K12n206
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-8 q^2+13 q-17+19 q^{-1} -18 q^{-2} +16 q^{-3} -11 q^{-4} +6 q^{-5} -2 q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-13 t^2+24 t-29+24 t^{-1} -13 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 115 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+a^4 z^6-6 a^2 z^6+2 z^6+5 a^4 z^4-15 a^2 z^4-z^4 a^{-2} +8 z^4-a^6 z^2+10 a^4 z^2-17 a^2 z^2-2 z^2 a^{-2} +11 z^2-2 a^6+6 a^4-7 a^2- a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+7 a^3 z^9+12 a z^9+5 z^9 a^{-1} +9 a^4 z^8+13 a^2 z^8+4 z^8 a^{-2} +8 z^8+5 a^5 z^7-11 a^3 z^7-30 a z^7-13 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-22 a^4 z^6-53 a^2 z^6-14 z^6 a^{-2} -44 z^6-5 a^5 z^5+a^3 z^5+12 a z^5+3 z^5 a^{-1} -3 z^5 a^{-3} +6 a^6 z^4+31 a^4 z^4+60 a^2 z^4+15 z^4 a^{-2} +50 z^4+3 a^7 z^3+8 a^5 z^3+4 a^3 z^3+4 a z^3+8 z^3 a^{-1} +3 z^3 a^{-3} -5 a^6 z^2-21 a^4 z^2-34 a^2 z^2-5 z^2 a^{-2} -23 z^2-2 a^7 z-3 a^5 z-2 a^3 z-3 a z-3 z a^{-1} -z a^{-3} +2 a^6+6 a^4+7 a^2+ a^{-2} +5 }[/math] |
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