K12a332
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-8+15 q^{-1} -21 q^{-2} +25 q^{-3} -27 q^{-4} +25 q^{-5} -19 q^{-6} +14 q^{-7} -8 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+41 t-57+41 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4+3 z^2+1 }[/math] |
| Determinant | 171 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+3 z^2 a^8+a^8-3 z^4 a^6-2 z^2 a^6+a^6+z^6 a^4-z^2 a^4-2 a^4+z^6 a^2+2 z^4 a^2+4 z^2 a^2+2 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-10 z^6 a^{10}+10 z^4 a^{10}-4 z^2 a^{10}+a^{10}+5 z^9 a^9-15 z^7 a^9+13 z^5 a^9-5 z^3 a^9+z a^9+4 z^{10} a^8-5 z^8 a^8-9 z^6 a^8+11 z^4 a^8-2 z^2 a^8+a^8+z^{11} a^7+12 z^9 a^7-42 z^7 a^7+46 z^5 a^7-24 z^3 a^7+4 z a^7+8 z^{10} a^6-9 z^8 a^6-10 z^6 a^6+9 z^4 a^6+3 z^2 a^6-a^6+z^{11} a^5+14 z^9 a^5-34 z^7 a^5+27 z^5 a^5-9 z^3 a^5-z a^5+4 z^{10} a^4+7 z^8 a^4-20 z^6 a^4+6 z^4 a^4+7 z^2 a^4-2 a^4+7 z^9 a^3-z^7 a^3-12 z^5 a^3+10 z^3 a^3-3 z a^3+8 z^8 a^2-5 z^6 a^2-8 z^4 a^2+9 z^2 a^2-2 a^2+7 z^7 a-9 z^5 a+4 z^3 a-z a+4 z^6-6 z^4+3 z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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