K12n521
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+4 q^5-8 q^4+12 q^3-15 q^2+16 q-14+12 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-14 t^2+18 t-17+18 t^{-1} -14 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+2 z^4+1 }[/math] |
| Determinant | 95 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-8 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-5 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +5 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+5 a z^9+10 z^9 a^{-1} +5 z^9 a^{-3} +4 a^2 z^8+5 z^8 a^{-2} +4 z^8 a^{-4} +5 z^8+a^3 z^7-14 a z^7-28 z^7 a^{-1} -12 z^7 a^{-3} +z^7 a^{-5} -14 a^2 z^6-30 z^6 a^{-2} -8 z^6 a^{-4} -36 z^6-3 a^3 z^5+3 a z^5+12 z^5 a^{-1} +10 z^5 a^{-3} +4 z^5 a^{-5} +14 a^2 z^4+31 z^4 a^{-2} +11 z^4 a^{-4} +4 z^4 a^{-6} +38 z^4+3 a^3 z^3+8 a z^3+7 z^3 a^{-1} -2 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} -5 a^2 z^2-9 z^2 a^{-2} -5 z^2 a^{-4} -2 z^2 a^{-6} -11 z^2-a^3 z-3 a z-3 z a^{-1} -z a^{-3} +1 }[/math] |
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