K12n461
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+4 q^2-7 q+11-13 q^{-1} +14 q^{-2} -13 q^{-3} +10 q^{-4} -7 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+7 t^2-20 t+29-20 t^{-1} +7 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+z^4-z^2+1 }[/math] |
| Determinant | 85 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6+2 z^4 a^4+3 z^2 a^4+a^4-z^6 a^2-3 z^4 a^2-5 z^2 a^2-2 a^2+2 z^4+3 z^2+2-z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{10}+3 a^2 z^{10}+6 a^5 z^9+12 a^3 z^9+6 a z^9+4 a^6 z^8-4 a^4 z^8-4 a^2 z^8+4 z^8+a^7 z^7-24 a^5 z^7-49 a^3 z^7-23 a z^7+z^7 a^{-1} -15 a^6 z^6-19 a^4 z^6-15 a^2 z^6-11 z^6-3 a^7 z^5+25 a^5 z^5+59 a^3 z^5+34 a z^5+3 z^5 a^{-1} +13 a^6 z^4+30 a^4 z^4+29 a^2 z^4+4 z^4 a^{-2} +16 z^4+a^7 z^3-8 a^5 z^3-24 a^3 z^3-20 a z^3-4 z^3 a^{-1} +z^3 a^{-3} -3 a^6 z^2-11 a^4 z^2-15 a^2 z^2-3 z^2 a^{-2} -10 z^2+2 a^3 z+3 a z+z a^{-1} +a^4+2 a^2+2 }[/math] |
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