K12n241
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+2 q^3-4 q^2+7 q-8+10 q^{-1} -9 q^{-2} +8 q^{-3} -6 q^{-4} +3 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-7 t^2+13 t-15+13 t^{-1} -7 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+5 z^4+3 z^2+1 }[/math] |
| Determinant | 59 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6+z^6-a^4 z^4+3 a^2 z^4-z^4 a^{-2} +4 z^4-2 a^4 z^2+2 a^2 z^2-3 z^2 a^{-2} +6 z^2-a^4-2 a^{-2} +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} +2 a^4 z^8-a^2 z^8+2 z^8 a^{-2} -z^8+a^5 z^7-5 a^3 z^7-14 a z^7-7 z^7 a^{-1} +z^7 a^{-3} -4 a^4 z^6-9 z^6 a^{-2} -5 z^6+7 a^3 z^5+17 a z^5+5 z^5 a^{-1} -5 z^5 a^{-3} +3 a^6 z^4+5 a^4 z^4-3 a^2 z^4+12 z^4 a^{-2} +7 z^4+a^7 z^3+2 a^5 z^3-5 a^3 z^3-12 a z^3+z^3 a^{-1} +7 z^3 a^{-3} -2 a^6 z^2+a^4 z^2+a^2 z^2-6 z^2 a^{-2} -8 z^2-a^7 z+2 a^3 z+a z-2 z a^{-1} -2 z a^{-3} -a^4+2 a^{-2} +4 }[/math] |
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