K12n448
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-6 q^3+11 q^2-15 q+18-18 q^{-1} +16 q^{-2} -12 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+14 t^2-21 t+25-21 t^{-1} +14 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^6-2 z^4-3 z^2+1 }[/math] |
| Determinant | 109 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-z^6 a^{-2} +5 z^6+a^4 z^4-8 a^2 z^4-4 z^4 a^{-2} +9 z^4+3 a^4 z^2-10 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +8 z^2+2 a^4-4 a^2-2 a^{-2} + a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+5 a^3 z^9+10 a z^9+5 z^9 a^{-1} +5 a^4 z^8+5 a^2 z^8+4 z^8 a^{-2} +4 z^8+3 a^5 z^7-11 a^3 z^7-27 a z^7-12 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-13 a^4 z^6-25 a^2 z^6-6 z^6 a^{-2} -17 z^6-8 a^5 z^5+8 a^3 z^5+33 a z^5+22 z^5 a^{-1} +5 z^5 a^{-3} -3 a^6 z^4+11 a^4 z^4+33 a^2 z^4+10 z^4 a^{-2} +3 z^4 a^{-4} +26 z^4+5 a^5 z^3-5 a^3 z^3-19 a z^3-17 z^3 a^{-1} -8 z^3 a^{-3} +2 a^6 z^2-7 a^4 z^2-20 a^2 z^2-9 z^2 a^{-2} -4 z^2 a^{-4} -16 z^2-a^5 z+a^3 z+4 a z+4 z a^{-1} +2 z a^{-3} +2 a^4+4 a^2+2 a^{-2} + a^{-4} +4 }[/math] |
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