K12a864
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-8 q^2+13 q-18+23 q^{-1} -24 q^{-2} +23 q^{-3} -19 q^{-4} +13 q^{-5} -8 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-5 t^4+12 t^3-20 t^2+27 t-29+27 t^{-1} -20 t^{-2} +12 t^{-3} -5 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+5 z^8+7 z^6+2 z^4+1 }[/math] |
| Determinant | 159 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+7 a^2 z^8-z^8-5 a^4 z^6+17 a^2 z^6-5 z^6-7 a^4 z^4+16 a^2 z^4-7 z^4-2 a^4 z^2+4 a^2 z^2-2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+7 a^4 z^{10}+14 a^2 z^{10}+7 z^{10}+8 a^5 z^9+a^3 z^9+7 z^9 a^{-1} +8 a^6 z^8-18 a^4 z^8-55 a^2 z^8+4 z^8 a^{-2} -25 z^8+7 a^7 z^7-14 a^5 z^7-24 a^3 z^7-30 a z^7-26 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-11 a^6 z^6+25 a^4 z^6+80 a^2 z^6-14 z^6 a^{-2} +26 z^6+a^9 z^5-11 a^7 z^5+9 a^5 z^5+42 a^3 z^5+49 a z^5+25 z^5 a^{-1} -3 z^5 a^{-3} -6 a^8 z^4+a^6 z^4-17 a^4 z^4-46 a^2 z^4+10 z^4 a^{-2} -12 z^4-a^9 z^3+3 a^7 z^3-2 a^5 z^3-22 a^3 z^3-25 a z^3-8 z^3 a^{-1} +z^3 a^{-3} +a^8 z^2+2 a^6 z^2+5 a^4 z^2+7 a^2 z^2-z^2 a^{-2} +2 z^2+a^5 z+3 a^3 z+3 a z+z a^{-1} +1 }[/math] |
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