K12a287
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+12 q-21+31 q^{-1} -36 q^{-2} +39 q^{-3} -36 q^{-4} +28 q^{-5} -19 q^{-6} +10 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-27 t^2+53 t-65+53 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^4+z^2+1 }[/math] |
| Determinant | 243 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-6 z^2 a^6-3 a^6+3 z^6 a^4+9 z^4 a^4+9 z^2 a^4+2 a^4-z^8 a^2-4 z^6 a^2-7 z^4 a^2-4 z^2 a^2+a^2+z^6+2 z^4+z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^5 z^{11}+2 a^3 z^{11}+7 a^6 z^{10}+15 a^4 z^{10}+8 a^2 z^{10}+10 a^7 z^9+24 a^5 z^9+27 a^3 z^9+13 a z^9+8 a^8 z^8+5 a^6 z^8-5 a^4 z^8+9 a^2 z^8+11 z^8+4 a^9 z^7-15 a^7 z^7-61 a^5 z^7-66 a^3 z^7-19 a z^7+5 z^7 a^{-1} +a^{10} z^6-15 a^8 z^6-35 a^6 z^6-49 a^4 z^6-52 a^2 z^6+z^6 a^{-2} -21 z^6-8 a^9 z^5+7 a^7 z^5+55 a^5 z^5+50 a^3 z^5+2 a z^5-8 z^5 a^{-1} -2 a^{10} z^4+10 a^8 z^4+40 a^6 z^4+64 a^4 z^4+50 a^2 z^4-z^4 a^{-2} +13 z^4+5 a^9 z^3-2 a^7 z^3-23 a^5 z^3-17 a^3 z^3+2 a z^3+3 z^3 a^{-1} +a^{10} z^2-4 a^8 z^2-19 a^6 z^2-26 a^4 z^2-16 a^2 z^2-4 z^2-a^9 z+5 a^5 z+5 a^3 z+a z+a^8+3 a^6+2 a^4-a^2 }[/math] |
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