K12n748
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+6 q^7-10 q^6+12 q^5-13 q^4+13 q^3-10 q^2+7 q-3+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-9 t^2+16 t-19+16 t^{-1} -9 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-5 z^4+1 }[/math] |
| Determinant | 79 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-4} +z^6 a^{-2} -6 z^6 a^{-4} +z^6 a^{-6} +4 z^4 a^{-2} -13 z^4 a^{-4} +4 z^4 a^{-6} +6 z^2 a^{-2} -11 z^2 a^{-4} +5 z^2 a^{-6} +3 a^{-2} -3 a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-3} +4 z^9 a^{-5} +3 z^9 a^{-7} -2 z^8 a^{-4} +2 z^8 a^{-6} +4 z^8 a^{-8} -8 z^7 a^{-5} -5 z^7 a^{-7} +3 z^7 a^{-9} +6 z^6 a^{-2} +14 z^6 a^{-4} -3 z^6 a^{-6} -10 z^6 a^{-8} +z^6 a^{-10} +3 z^5 a^{-1} +6 z^5 a^{-3} +13 z^5 a^{-5} +z^5 a^{-7} -9 z^5 a^{-9} -9 z^4 a^{-2} -24 z^4 a^{-4} -6 z^4 a^{-6} +5 z^4 a^{-8} -3 z^4 a^{-10} +z^4-3 z^3 a^{-1} -8 z^3 a^{-3} -14 z^3 a^{-5} -2 z^3 a^{-7} +7 z^3 a^{-9} +8 z^2 a^{-2} +16 z^2 a^{-4} +5 z^2 a^{-6} +2 z^2 a^{-10} -z^2+z a^{-1} +4 z a^{-3} +4 z a^{-5} -z a^{-9} -3 a^{-2} -3 a^{-4} - a^{-6} }[/math] |
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