K12n258
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+q^4+2 q-2+3 q^{-1} -4 q^{-2} +3 q^{-3} -2 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^2+4 t-5+4 t^{-1} - t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-z^4 }[/math] |
| Determinant | 15 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^4+a^4-z^4 a^2-2 z^2 a^2-a^2-z^4-3 z^2-2+z^4 a^{-2} +5 z^2 a^{-2} +5 a^{-2} -z^2 a^{-4} -2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+2 a^3 z^9+4 a z^9+2 z^9 a^{-1} +a^4 z^8-3 a^2 z^8+z^8 a^{-2} -3 z^8-12 a^3 z^7-24 a z^7-12 z^7 a^{-1} -6 a^4 z^6-7 a^2 z^6-6 z^6 a^{-2} +z^6 a^{-4} -8 z^6+22 a^3 z^5+41 a z^5+18 z^5 a^{-1} +z^5 a^{-5} +11 a^4 z^4+22 a^2 z^4+4 z^4 a^{-2} -5 z^4 a^{-4} +20 z^4-16 a^3 z^3-27 a z^3-12 z^3 a^{-1} -5 z^3 a^{-3} -4 z^3 a^{-5} -7 a^4 z^2-14 a^2 z^2+5 z^2 a^{-2} +4 z^2 a^{-4} -6 z^2+4 a^3 z+8 a z+6 z a^{-1} +4 z a^{-3} +2 z a^{-5} +a^4+a^2-5 a^{-2} -2 a^{-4} -2 }[/math] |
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