K12n815
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+2 q^4-q^3+q-2+3 q^{-1} -3 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^2+2 t-1+2 t^{-1} - t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^4-2 z^2+1 }[/math] |
| Determinant | 7 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} +z^6-a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +5 z^4-2 a^2 z^2-10 z^2 a^{-2} +3 z^2 a^{-4} +7 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^9+2 z^9 a^{-1} +3 a^2 z^8+3 z^8 a^{-2} +z^8 a^{-4} +5 z^8+a^3 z^7-9 a z^7-11 z^7 a^{-1} +z^7 a^{-3} +2 z^7 a^{-5} -15 a^2 z^6-21 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} -30 z^6-4 a^3 z^5+5 a z^5+10 z^5 a^{-1} -8 z^5 a^{-3} -9 z^5 a^{-5} +18 a^2 z^4+37 z^4 a^{-2} +5 z^4 a^{-4} -4 z^4 a^{-6} +46 z^4+3 a^3 z^3+6 a z^3+4 z^3 a^{-1} +9 z^3 a^{-3} +8 z^3 a^{-5} -6 a^2 z^2-23 z^2 a^{-2} -5 z^2 a^{-4} +3 z^2 a^{-6} -21 z^2-a^3 z-3 a z-3 z a^{-1} -3 z a^{-3} -2 z a^{-5} +4 a^{-2} +2 a^{-4} +3 }[/math] |
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