K12n497
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-8 q^3+12 q^2-16 q+18-16 q^{-1} +14 q^{-2} -9 q^{-3} +5 q^{-4} -2 q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+9 t^2-25 t+35-25 t^{-1} +9 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+3 z^4+2 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6+3 a^2 z^4+2 z^4 a^{-2} -2 z^4-2 a^4 z^2+6 a^2 z^2+2 z^2 a^{-2} -z^2 a^{-4} -3 z^2-2 a^4+4 a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+2 a^3 z^9+6 a z^9+4 z^9 a^{-1} +a^4 z^8+3 a^2 z^8+7 z^8 a^{-2} +9 z^8-3 a^3 z^7-9 a z^7+z^7 a^{-1} +7 z^7 a^{-3} +2 a^4 z^6-3 a^2 z^6-10 z^6 a^{-2} +4 z^6 a^{-4} -19 z^6+3 a^5 z^5+9 a^3 z^5+10 a z^5-9 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} -8 a^4 z^4-5 a^2 z^4+4 z^4 a^{-2} -6 z^4 a^{-4} +13 z^4-7 a^5 z^3-17 a^3 z^3-12 a z^3+4 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} +6 a^4 z^2+7 a^2 z^2-z^2 a^{-2} +z^2 a^{-4} -z^2+4 a^5 z+8 a^3 z+6 a z+2 z a^{-1} -2 a^4-4 a^2-1 }[/math] |
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