K12n864
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^7-6 q^6+12 q^5-18 q^4+21 q^3-22 q^2+20 q-15+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-15 t^2+28 t-33+28 t^{-1} -15 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-5 z^4-3 z^2+1 }[/math] |
| Determinant | 131 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +z^6-10 z^4 a^{-2} +2 z^4 a^{-4} +3 z^4-9 z^2 a^{-2} +z^2 a^{-4} +z^2 a^{-6} +4 z^2-3 a^{-2} + a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +7 z^9 a^{-1} +11 z^9 a^{-3} +4 z^9 a^{-5} +13 z^8 a^{-2} +8 z^8 a^{-4} +3 z^8 a^{-6} +8 z^8+4 a z^7-10 z^7 a^{-1} -14 z^7 a^{-3} +z^7 a^{-5} +z^7 a^{-7} +a^2 z^6-38 z^6 a^{-2} -15 z^6 a^{-4} +3 z^6 a^{-6} -19 z^6-8 a z^5-2 z^5 a^{-1} -5 z^5 a^{-3} -6 z^5 a^{-5} +5 z^5 a^{-7} -2 a^2 z^4+29 z^4 a^{-2} +4 z^4 a^{-4} -5 z^4 a^{-6} +3 z^4 a^{-8} +15 z^4+4 a z^3+2 z^3 a^{-1} +10 z^3 a^{-3} +7 z^3 a^{-5} -5 z^3 a^{-7} +a^2 z^2-13 z^2 a^{-2} +3 z^2 a^{-4} +4 z^2 a^{-6} -3 z^2 a^{-8} -8 z^2-z a^{-1} -4 z a^{-3} -2 z a^{-5} +z a^{-7} +3 a^{-2} - a^{-6} +3 }[/math] |
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