K12n391
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+14 q^{-1} -17 q^{-2} +20 q^{-3} -18 q^{-4} +15 q^{-5} -10 q^{-6} +5 q^{-7} -2 q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-12 t^2+26 t-33+26 t^{-1} -12 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+6 z^4+5 z^2+1 }[/math] |
| Determinant | 115 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^4 a^6-5 z^2 a^6-4 a^6+2 z^6 a^4+8 z^4 a^4+13 z^2 a^4+7 a^4+z^6 a^2+z^4 a^2-2 z^2 a^2-2 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^6 z^{10}+a^4 z^{10}+2 a^7 z^9+7 a^5 z^9+5 a^3 z^9+a^8 z^8+6 a^6 z^8+14 a^4 z^8+9 a^2 z^8-a^7 z^7-7 a^5 z^7+2 a^3 z^7+8 a z^7+2 a^8 z^6-15 a^6 z^6-36 a^4 z^6-15 a^2 z^6+4 z^6+3 a^9 z^5+2 a^7 z^5-5 a^5 z^5-18 a^3 z^5-13 a z^5+z^5 a^{-1} -6 a^8 z^4+17 a^6 z^4+38 a^4 z^4+10 a^2 z^4-5 z^4-7 a^9 z^3-6 a^7 z^3+11 a^5 z^3+17 a^3 z^3+6 a z^3-z^3 a^{-1} +2 a^8 z^2-13 a^6 z^2-22 a^4 z^2-6 a^2 z^2+z^2+4 a^9 z+2 a^7 z-5 a^5 z-5 a^3 z-2 a z+4 a^6+7 a^4+2 a^2 }[/math] |
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