K12n874
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-5 q^6+11 q^5-16 q^4+20 q^3-21 q^2+19 q-15+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-14 t^2+26 t-31+26 t^{-1} -14 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-4 z^4-z^2+1 }[/math] |
| Determinant | 123 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +z^6-10 z^4 a^{-2} +3 z^4 a^{-4} +3 z^4-10 z^2 a^{-2} +5 z^2 a^{-4} +4 z^2-5 a^{-2} +4 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +7 z^9 a^{-1} +11 z^9 a^{-3} +4 z^9 a^{-5} +13 z^8 a^{-2} +7 z^8 a^{-4} +2 z^8 a^{-6} +8 z^8+4 a z^7-10 z^7 a^{-1} -19 z^7 a^{-3} -5 z^7 a^{-5} +a^2 z^6-45 z^6 a^{-2} -24 z^6 a^{-4} +z^6 a^{-6} -19 z^6-8 a z^5-6 z^5 a^{-1} +3 z^5 a^{-3} +6 z^5 a^{-5} +5 z^5 a^{-7} -2 a^2 z^4+45 z^4 a^{-2} +32 z^4 a^{-4} +4 z^4 a^{-6} +z^4 a^{-8} +14 z^4+4 a z^3+7 z^3 a^{-1} +9 z^3 a^{-3} +3 z^3 a^{-5} -3 z^3 a^{-7} +a^2 z^2-24 z^2 a^{-2} -18 z^2 a^{-4} -5 z^2 a^{-6} -z^2 a^{-8} -9 z^2-a z-2 z a^{-1} -3 z a^{-3} -3 z a^{-5} -z a^{-7} +5 a^{-2} +4 a^{-4} + a^{-6} +3 }[/math] |
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