K12a782
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+8 q^5-13 q^4+19 q^3-22 q^2+23 q-21+17 q^{-1} -12 q^{-2} +7 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+36 t-47+36 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 151 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-2 a^2 z^4+z^4 a^{-2} -2 z^4 a^{-4} +z^4+a^4 z^2-3 a^2 z^2+z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} +a^4-a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+7 z^{10} a^{-2} +11 z^{10}+3 a^3 z^9+2 a z^9+10 z^9 a^{-1} +11 z^9 a^{-3} +a^4 z^8-15 a^2 z^8-10 z^8 a^{-2} +12 z^8 a^{-4} -38 z^8-14 a^3 z^7-34 a z^7-51 z^7 a^{-1} -20 z^7 a^{-3} +11 z^7 a^{-5} -5 a^4 z^6+12 a^2 z^6-8 z^6 a^{-2} -16 z^6 a^{-4} +8 z^6 a^{-6} +33 z^6+21 a^3 z^5+55 a z^5+57 z^5 a^{-1} +7 z^5 a^{-3} -12 z^5 a^{-5} +4 z^5 a^{-7} +8 a^4 z^4+5 a^2 z^4+7 z^4 a^{-2} -7 z^4 a^{-6} +z^4 a^{-8} -4 z^4-13 a^3 z^3-29 a z^3-22 z^3 a^{-1} -2 z^3 a^{-3} +2 z^3 a^{-5} -2 z^3 a^{-7} -5 a^4 z^2-7 a^2 z^2+2 z^2 a^{-2} +3 z^2 a^{-4} +2 z^2 a^{-6} -z^2+3 a^3 z+5 a z+3 z a^{-1} +z a^{-3} +a^4+a^2- a^{-2} }[/math] |
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