K12a49
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-10+19 q^{-1} -28 q^{-2} +35 q^{-3} -36 q^{-4} +35 q^{-5} -28 q^{-6} +19 q^{-7} -11 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^3-23 t^2+53 t-69+53 t^{-1} -23 t^{-2} +5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^6+7 z^4+6 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8-a^8+z^6 a^6-2 z^2 a^6-2 a^6+3 z^6 a^4+9 z^4 a^4+12 z^2 a^4+6 a^4+z^6 a^2-2 z^2 a^2-2 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-11 z^6 a^{10}+10 z^4 a^{10}-3 z^2 a^{10}+8 z^9 a^9-22 z^7 a^9+21 z^5 a^9-11 z^3 a^9+5 z a^9+7 z^{10} a^8-7 z^8 a^8-17 z^6 a^8+21 z^4 a^8-5 z^2 a^8-a^8+2 z^{11} a^7+21 z^9 a^7-68 z^7 a^7+63 z^5 a^7-29 z^3 a^7+7 z a^7+15 z^{10} a^6-12 z^8 a^6-42 z^6 a^6+54 z^4 a^6-23 z^2 a^6+2 a^6+2 z^{11} a^5+27 z^9 a^5-68 z^7 a^5+46 z^5 a^5-9 z^3 a^5-z a^5+8 z^{10} a^4+13 z^8 a^4-61 z^6 a^4+65 z^4 a^4-30 z^2 a^4+6 a^4+14 z^9 a^3-14 z^7 a^3-5 z^5 a^3+14 z^3 a^3-4 z a^3+14 z^8 a^2-21 z^6 a^2+18 z^4 a^2-8 z^2 a^2+2 a^2+9 z^7 a-11 z^5 a+7 z^3 a-2 z a+4 z^6-4 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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