K12a451
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-12 q^6+21 q^5-31 q^4+37 q^3-38 q^2+36 q-28+19 q^{-1} -10 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-27 t^2+53 t-65+53 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^4+z^2+1 }[/math] |
| Determinant | 243 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-8 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-7 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +7 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +15 z^{10} a^{-2} +9 z^{10} a^{-4} +6 z^{10}+7 a z^9+20 z^9 a^{-1} +30 z^9 a^{-3} +17 z^9 a^{-5} +4 a^2 z^8-7 z^8 a^{-2} +16 z^8 a^{-4} +18 z^8 a^{-6} -z^8+a^3 z^7-17 a z^7-59 z^7 a^{-1} -68 z^7 a^{-3} -15 z^7 a^{-5} +12 z^7 a^{-7} -12 a^2 z^6-53 z^6 a^{-2} -63 z^6 a^{-4} -24 z^6 a^{-6} +5 z^6 a^{-8} -31 z^6-3 a^3 z^5+11 a z^5+43 z^5 a^{-1} +34 z^5 a^{-3} -9 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+61 z^4 a^{-2} +48 z^4 a^{-4} +12 z^4 a^{-6} -3 z^4 a^{-8} +41 z^4+3 a^3 z^3+a z^3-6 z^3 a^{-1} +9 z^3 a^{-5} +5 z^3 a^{-7} -6 a^2 z^2-21 z^2 a^{-2} -12 z^2 a^{-4} -3 z^2 a^{-6} -18 z^2-a^3 z-2 a z-2 z a^{-1} -z a^{-3} +a^2+ a^{-2} +3 }[/math] |
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