K12a480
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+13 q^7-24 q^6+35 q^5-43 q^4+46 q^3-43 q^2+35 q-23+13 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-30 t^2+64 t-81+64 t^{-1} -30 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^4+1 }[/math] |
| Determinant | 287 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +3 z^6 a^{-4} +z^6-8 z^4 a^{-2} +7 z^4 a^{-4} -3 z^4 a^{-6} +2 z^4-5 z^2 a^{-2} +5 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} +2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +11 z^{10} a^{-2} +22 z^{10} a^{-4} +11 z^{10} a^{-6} +16 z^9 a^{-1} +35 z^9 a^{-3} +35 z^9 a^{-5} +16 z^9 a^{-7} +5 z^8 a^{-2} -13 z^8 a^{-4} +6 z^8 a^{-6} +12 z^8 a^{-8} +12 z^8+5 a z^7-27 z^7 a^{-1} -88 z^7 a^{-3} -86 z^7 a^{-5} -25 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-48 z^6 a^{-2} -51 z^6 a^{-4} -48 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -22 z^6-7 a z^5+16 z^5 a^{-1} +68 z^5 a^{-3} +64 z^5 a^{-5} +12 z^5 a^{-7} -7 z^5 a^{-9} -a^2 z^4+46 z^4 a^{-2} +56 z^4 a^{-4} +41 z^4 a^{-6} +14 z^4 a^{-8} -z^4 a^{-10} +15 z^4+2 a z^3-5 z^3 a^{-1} -21 z^3 a^{-3} -21 z^3 a^{-5} -4 z^3 a^{-7} +3 z^3 a^{-9} -13 z^2 a^{-2} -15 z^2 a^{-4} -11 z^2 a^{-6} -4 z^2 a^{-8} -5 z^2+z a^{-1} +3 z a^{-3} +3 z a^{-5} +z a^{-7} +1 }[/math] |
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