K12n465
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+4 q^5-8 q^4+11 q^3-13 q^2+14 q-12+10 q^{-1} -6 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-13 t^2+15 t-13+15 t^{-1} -13 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 83 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-8 z^4 a^{-2} +4 z^4 a^{-4} +8 z^4-3 a^2 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +8 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+4 a z^9+9 z^9 a^{-1} +5 z^9 a^{-3} +3 a^2 z^8+z^8 a^{-2} +4 z^8 a^{-4} +a^3 z^7-14 a z^7-32 z^7 a^{-1} -16 z^7 a^{-3} +z^7 a^{-5} -12 a^2 z^6-18 z^6 a^{-2} -9 z^6 a^{-4} -21 z^6-4 a^3 z^5+11 a z^5+33 z^5 a^{-1} +22 z^5 a^{-3} +4 z^5 a^{-5} +14 a^2 z^4+22 z^4 a^{-2} +11 z^4 a^{-4} +4 z^4 a^{-6} +29 z^4+4 a^3 z^3-a z^3-13 z^3 a^{-1} -13 z^3 a^{-3} -4 z^3 a^{-5} +z^3 a^{-7} -7 a^2 z^2-9 z^2 a^{-2} -4 z^2 a^{-4} -2 z^2 a^{-6} -14 z^2-a^3 z-a z+z a^{-1} +2 z a^{-3} +z a^{-5} +a^2+ a^{-2} +3 }[/math] |
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