K12n52
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-10+15 q^{-1} -19 q^{-2} +21 q^{-3} -19 q^{-4} +16 q^{-5} -10 q^{-6} +5 q^{-7} -2 q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-9 t^2+30 t-43+30 t^{-1} -9 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-3 z^4+3 z^2+1 }[/math] |
| Determinant | 123 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 a^8+5 z^2 a^6+4 a^6-4 z^4 a^4-6 z^2 a^4-3 a^4+z^6 a^2+2 z^4 a^2+4 z^2 a^2+2 a^2-z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^6 z^{10}+a^4 z^{10}+2 a^7 z^9+7 a^5 z^9+5 a^3 z^9+a^8 z^8+6 a^6 z^8+15 a^4 z^8+10 a^2 z^8-a^7 z^7-3 a^5 z^7+8 a^3 z^7+10 a z^7+2 a^8 z^6-10 a^6 z^6-28 a^4 z^6-11 a^2 z^6+5 z^6+3 a^9 z^5+4 a^7 z^5-12 a^5 z^5-29 a^3 z^5-15 a z^5+z^5 a^{-1} -6 a^8 z^4+2 a^6 z^4+9 a^4 z^4-4 a^2 z^4-5 z^4-7 a^9 z^3-9 a^7 z^3+11 a^5 z^3+17 a^3 z^3+4 a z^3+4 a^8 z^2+6 a^6 z^2+7 a^4 z^2+5 a^2 z^2+4 a^9 z+4 a^7 z-a^5 z-a^3 z-2 a^8-4 a^6-3 a^4-2 a^2 }[/math] |
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