K12n501
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+2 q^2-4 q+7-7 q^{-1} +8 q^{-2} -7 q^{-3} +6 q^{-4} -4 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-12 t+17-12 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4+4 z^2+1 }[/math] |
| Determinant | 49 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+z^4 a^4+z^2 a^4+2 z^4 a^2+4 z^2 a^2+2 a^2+z^4+z^2+1-z^2 a^{-2} - a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+2 a^5 z^9+4 a^3 z^9+2 a z^9+2 a^6 z^8-2 a^4 z^8-2 a^2 z^8+2 z^8+a^7 z^7-8 a^5 z^7-18 a^3 z^7-8 a z^7+z^7 a^{-1} -9 a^6 z^6-2 a^4 z^6-a^2 z^6-8 z^6-5 a^7 z^5+9 a^5 z^5+30 a^3 z^5+13 a z^5-3 z^5 a^{-1} +11 a^6 z^4+2 a^4 z^4+2 a^2 z^4+2 z^4 a^{-2} +13 z^4+7 a^7 z^3-6 a^5 z^3-27 a^3 z^3-9 a z^3+6 z^3 a^{-1} +z^3 a^{-3} -4 a^6 z^2-2 a^4 z^2+a^2 z^2-3 z^2 a^{-2} -4 z^2-2 a^7 z+2 a^5 z+8 a^3 z+4 a z-2 z a^{-1} -2 z a^{-3} +a^6-2 a^2+ a^{-2} +1 }[/math] |
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