K12a569
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-7 q^{-1} +12 q^{-2} -18 q^{-3} +22 q^{-4} -23 q^{-5} +23 q^{-6} -18 q^{-7} +13 q^{-8} -8 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+21 t^2-31 t+33-31 t^{-1} +21 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-z^4+6 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-2 a^{10}+3 z^4 a^8+8 z^2 a^8+3 a^8-3 z^6 a^6-11 z^4 a^6-10 z^2 a^6-2 a^6+z^8 a^4+5 z^6 a^4+10 z^4 a^4+10 z^2 a^4+2 a^4-z^6 a^2-3 z^4 a^2-z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-10 z^5 a^{11}+8 z^3 a^{11}-4 z a^{11}+7 z^8 a^{10}-9 z^6 a^{10}+5 z^4 a^{10}-4 z^2 a^{10}+2 a^{10}+6 z^9 a^9-4 z^7 a^9-5 z^5 a^9+7 z^3 a^9-3 z a^9+4 z^{10} a^8-8 z^6 a^8+7 z^4 a^8-4 z^2 a^8+3 a^8+z^{11} a^7+12 z^9 a^7-41 z^7 a^7+54 z^5 a^7-32 z^3 a^7+5 z a^7+8 z^{10} a^6-16 z^8 a^6-z^6 a^6+19 z^4 a^6-11 z^2 a^6+2 a^6+z^{11} a^5+12 z^9 a^5-54 z^7 a^5+74 z^5 a^5-39 z^3 a^5+4 z a^5+4 z^{10} a^4-5 z^8 a^4-20 z^6 a^4+35 z^4 a^4-15 z^2 a^4+2 a^4+6 z^9 a^3-22 z^7 a^3+23 z^5 a^3-9 z^3 a^3+z a^3+4 z^8 a^2-15 z^6 a^2+14 z^4 a^2-3 z^2 a^2+z^7 a-3 z^5 a+z^3 a }[/math] |
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