K12n678
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+10 q^5-12 q^4+14 q^3-12 q^2+10 q-6+3 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-8 t^2+18 t-23+18 t^{-1} -8 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+4 z^4+4 z^2+1 }[/math] |
| Determinant | 79 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +3 z^4 a^{-2} +3 z^4 a^{-4} -z^4 a^{-6} -z^4+4 z^2 a^{-2} +4 z^2 a^{-4} -2 z^2 a^{-6} -2 z^2+2 a^{-2} +2 a^{-4} -2 a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +4 z^9 a^{-3} +3 z^9 a^{-5} -3 z^8 a^{-2} +2 z^8 a^{-4} +5 z^8 a^{-6} -3 z^7 a^{-1} -11 z^7 a^{-3} -3 z^7 a^{-5} +5 z^7 a^{-7} +11 z^6 a^{-2} -4 z^6 a^{-4} -9 z^6 a^{-6} +3 z^6 a^{-8} +3 z^6+a z^5+10 z^5 a^{-1} +20 z^5 a^{-3} +z^5 a^{-5} -9 z^5 a^{-7} +z^5 a^{-9} -14 z^4 a^{-2} +5 z^4 a^{-4} +7 z^4 a^{-6} -5 z^4 a^{-8} -7 z^4-3 a z^3-14 z^3 a^{-1} -15 z^3 a^{-3} +2 z^3 a^{-5} +4 z^3 a^{-7} -2 z^3 a^{-9} +7 z^2 a^{-2} -3 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +4 z^2+2 a z+5 z a^{-1} +4 z a^{-3} -2 z a^{-5} -2 z a^{-7} +z a^{-9} -2 a^{-2} +2 a^{-4} +2 a^{-6} -1 }[/math] |
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