K12a70
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+5-11 q^{-1} +20 q^{-2} -28 q^{-3} +35 q^{-4} -37 q^{-5} +34 q^{-6} -28 q^{-7} +19 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+27 t^2-50 t+61-50 t^{-1} +27 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^4+2 z^2+1 }[/math] |
| Determinant | 233 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-a^{10}+3 z^4 a^8+6 z^2 a^8+3 a^8-3 z^6 a^6-9 z^4 a^6-9 z^2 a^6-4 a^6+z^8 a^4+4 z^6 a^4+7 z^4 a^4+6 z^2 a^4+2 a^4-z^6 a^2-2 z^4 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+9 z^7 a^{11}-11 z^5 a^{11}+7 z^3 a^{11}-2 z a^{11}+14 z^8 a^{10}-21 z^6 a^{10}+17 z^4 a^{10}-6 z^2 a^{10}+a^{10}+14 z^9 a^9-15 z^7 a^9-z^5 a^9+9 z^3 a^9-3 z a^9+8 z^{10} a^8+12 z^8 a^8-56 z^6 a^8+56 z^4 a^8-22 z^2 a^8+3 a^8+2 z^{11} a^7+27 z^9 a^7-68 z^7 a^7+47 z^5 a^7-11 z^3 a^7-z a^7+15 z^{10} a^6-10 z^8 a^6-50 z^6 a^6+64 z^4 a^6-28 z^2 a^6+4 a^6+2 z^{11} a^5+22 z^9 a^5-69 z^7 a^5+56 z^5 a^5-16 z^3 a^5+z a^5+7 z^{10} a^4-3 z^8 a^4-33 z^6 a^4+41 z^4 a^4-15 z^2 a^4+2 a^4+9 z^9 a^3-24 z^7 a^3+18 z^5 a^3-3 z^3 a^3+z a^3+5 z^8 a^2-14 z^6 a^2+12 z^4 a^2-2 z^2 a^2-a^2+z^7 a-2 z^5 a+z^3 a }[/math] |
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