K12n257
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+q^3-q+4-4 q^{-1} +5 q^{-2} -5 q^{-3} +4 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^2-6 t+9-6 t^{-1} +2 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^4+2 z^2+1 }[/math] |
| Determinant | 25 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6+z^6+a^4 z^4-5 a^2 z^4-z^4 a^{-2} +7 z^4+2 a^4 z^2-9 a^2 z^2-4 z^2 a^{-2} +13 z^2+a^4-5 a^2-3 a^{-2} +8 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^8+a^2 z^8+z^8 a^{-2} +3 a^5 z^7+5 a^3 z^7+a z^7+z^7 a^{-3} +a^6 z^6-5 a^4 z^6-2 a^2 z^6-7 z^6 a^{-2} -3 z^6-11 a^5 z^5-17 a^3 z^5-4 a z^5-4 z^5 a^{-1} -6 z^5 a^{-3} -3 a^6 z^4-a^4 z^4+3 a^2 z^4+13 z^4 a^{-2} +14 z^4+9 a^5 z^3+14 a^3 z^3+8 a z^3+12 z^3 a^{-1} +9 z^3 a^{-3} +2 a^6 z^2+2 a^4 z^2-9 a^2 z^2-8 z^2 a^{-2} -17 z^2-a^5 z-4 a^3 z-6 a z-6 z a^{-1} -3 z a^{-3} +a^4+5 a^2+3 a^{-2} +8 }[/math] |
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