K12a889
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-4 q^4+8 q^3-14 q^2+20 q-23+26 q^{-1} -24 q^{-2} +20 q^{-3} -14 q^{-4} +8 q^{-5} -4 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-22 t^2+32 t-35+32 t^{-1} -22 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-2 z^4+2 z^2+1 }[/math] |
| Determinant | 167 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-4 a^2 z^6+z^6 a^{-2} -4 z^6+3 a^4 z^4-4 a^2 z^4+3 z^4 a^{-2} -4 z^4+a^4 z^2+z^2 a^{-2} -a^4+a^2- a^{-2} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +9 a^2 z^{10}+6 z^{10} a^{-2} +15 z^{10}+14 a^3 z^9+9 a z^9-z^9 a^{-1} +4 z^9 a^{-3} +15 a^4 z^8-14 a^2 z^8-26 z^8 a^{-2} +z^8 a^{-4} -56 z^8+12 a^5 z^7-30 a^3 z^7-56 a z^7-32 z^7 a^{-1} -18 z^7 a^{-3} +8 a^6 z^6-28 a^4 z^6-14 a^2 z^6+36 z^6 a^{-2} -4 z^6 a^{-4} +62 z^6+4 a^7 z^5-14 a^5 z^5+15 a^3 z^5+62 a z^5+54 z^5 a^{-1} +25 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+16 a^4 z^4+22 a^2 z^4-20 z^4 a^{-2} +4 z^4 a^{-4} -25 z^4-2 a^7 z^3+2 a^5 z^3-a^3 z^3-20 a z^3-26 z^3 a^{-1} -11 z^3 a^{-3} -3 a^4 z^2-4 a^2 z^2+3 z^2 a^{-2} +2 z^2+a^5 z+a^3 z+a z+z a^{-1} -a^4-a^2+ a^{-2} +2 }[/math] |
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