K12a999
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-8 q^2+14 q-20+26 q^{-1} -26 q^{-2} +26 q^{-3} -21 q^{-4} +14 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+11 t^3-21 t^2+31 t-35+31 t^{-1} -21 t^{-2} +11 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+14 z^6+15 z^4+7 z^2+1 }[/math] |
| Determinant | 171 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+8 a^2 z^8-z^8-6 a^4 z^6+26 a^2 z^6-6 z^6-14 a^4 z^4+43 a^2 z^4-14 z^4-15 a^4 z^2+37 a^2 z^2-15 z^2-7 a^4+14 a^2-6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+11 a^2 z^{10}+5 z^{10}+8 a^5 z^9+8 a^3 z^9+5 a z^9+5 z^9 a^{-1} +8 a^6 z^8-8 a^4 z^8-32 a^2 z^8+3 z^8 a^{-2} -13 z^8+6 a^7 z^7-10 a^5 z^7-26 a^3 z^7-26 a z^7-15 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-11 a^6 z^6+15 a^4 z^6+54 a^2 z^6-10 z^6 a^{-2} +15 z^6+a^9 z^5-9 a^7 z^5+5 a^5 z^5+36 a^3 z^5+38 a z^5+13 z^5 a^{-1} -4 z^5 a^{-3} -4 a^8 z^4+7 a^6 z^4-28 a^4 z^4-69 a^2 z^4+9 z^4 a^{-2} -21 z^4-2 a^9 z^3+7 a^7 z^3+a^5 z^3-36 a^3 z^3-38 a z^3-5 z^3 a^{-1} +5 z^3 a^{-3} +a^8 z^2+24 a^4 z^2+44 a^2 z^2-z^2 a^{-2} +18 z^2+a^9 z-3 a^7 z+a^5 z+15 a^3 z+15 a z+3 z a^{-1} -2 z a^{-3} -7 a^4-14 a^2-6 }[/math] |
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