K12n804
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^7-5 q^6+9 q^5-13 q^4+15 q^3-16 q^2+14 q-10+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-11 t^2+20 t-23+20 t^{-1} -11 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-7 z^4-4 z^2+1 }[/math] |
| Determinant | 95 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +z^6-14 z^4 a^{-2} +3 z^4 a^{-4} +4 z^4-14 z^2 a^{-2} +3 z^2 a^{-4} +z^2 a^{-6} +6 z^2-5 a^{-2} + a^{-4} + a^{-6} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +4 z^9 a^{-1} +6 z^9 a^{-3} +2 z^9 a^{-5} +8 z^8 a^{-2} +5 z^8 a^{-4} +2 z^8 a^{-6} +5 z^8+3 a z^7-8 z^7 a^{-1} -9 z^7 a^{-3} +3 z^7 a^{-5} +z^7 a^{-7} +a^2 z^6-30 z^6 a^{-2} -12 z^6 a^{-4} +2 z^6 a^{-6} -15 z^6-8 a z^5+3 z^5 a^{-1} -4 z^5 a^{-3} -12 z^5 a^{-5} +3 z^5 a^{-7} -3 a^2 z^4+38 z^4 a^{-2} +10 z^4 a^{-4} -6 z^4 a^{-6} +3 z^4 a^{-8} +16 z^4+4 a z^3+17 z^3 a^{-3} +16 z^3 a^{-5} -5 z^3 a^{-7} +2 a^2 z^2-23 z^2 a^{-2} -z^2 a^{-4} +4 z^2 a^{-6} -4 z^2 a^{-8} -12 z^2-2 z a^{-1} -8 z a^{-3} -6 z a^{-5} +5 a^{-2} + a^{-4} - a^{-6} +4 }[/math] |
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