K12a379
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+2 q-3+6 q^{-1} -8 q^{-2} +10 q^{-3} -10 q^{-4} +10 q^{-5} -8 q^{-6} +6 q^{-7} -4 q^{-8} +2 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-9 t^2+15 t-17+15 t^{-1} -9 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+9 z^4+6 z^2+1 }[/math] |
| Determinant | 71 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-2 a^8+z^6 a^6+4 z^4 a^6+5 z^2 a^6+2 a^6+z^6 a^4+3 z^4 a^4+2 z^2 a^4+z^6 a^2+4 z^4 a^2+5 z^2 a^2+2 a^2-z^4-3 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+7 z^3 a^{11}-3 z a^{11}+2 z^8 a^{10}-9 z^6 a^{10}+10 z^4 a^{10}-2 z^2 a^{10}+2 z^9 a^9-7 z^7 a^9+3 z^5 a^9+3 z^3 a^9+2 z^{10} a^8-9 z^8 a^8+16 z^6 a^8-20 z^4 a^8+12 z^2 a^8-2 a^8+z^{11} a^7-3 z^9 a^7+z^7 a^7+6 z^5 a^7-12 z^3 a^7+4 z a^7+4 z^{10} a^6-22 z^8 a^6+49 z^6 a^6-48 z^4 a^6+16 z^2 a^6-2 a^6+z^{11} a^5-3 z^9 a^5+z^7 a^5+10 z^5 a^5-10 z^3 a^5+z a^5+2 z^{10} a^4-9 z^8 a^4+18 z^6 a^4-12 z^4 a^4+4 z^2 a^4+2 z^9 a^3-6 z^7 a^3+7 z^5 a^3+z^3 a^3+2 z^8 a^2-4 z^6 a^2+6 z^2 a^2-2 a^2+2 z^7 a-4 z^5 a+z a+2 z^6-6 z^4+4 z^2-1+z^5 a^{-1} -3 z^3 a^{-1} +z a^{-1} }[/math] |
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