K12n792
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^3-4 q^2+7 q-10+12 q^{-1} -13 q^{-2} +12 q^{-3} -9 q^{-4} +6 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-10 t^2+16 t-17+16 t^{-1} -10 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-6 z^4-4 z^2+1 }[/math] |
| Determinant | 79 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+a^4 z^6-6 a^2 z^6+z^6+4 a^4 z^4-13 a^2 z^4+3 z^4+5 a^4 z^2-11 a^2 z^2+z^2 a^{-2} +z^2+2 a^4-2 a^2+2 a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+4 a^3 z^9+5 a z^9+z^9 a^{-1} +6 a^4 z^8+5 a^2 z^8-z^8+6 a^5 z^7-8 a^3 z^7-15 a z^7-z^7 a^{-1} +5 a^6 z^6-13 a^4 z^6-22 a^2 z^6+3 z^6 a^{-2} -z^6+3 a^7 z^5-9 a^5 z^5+7 a^3 z^5+14 a z^5-5 z^5 a^{-1} +a^8 z^4-6 a^6 z^4+15 a^4 z^4+27 a^2 z^4-11 z^4 a^{-2} -6 z^4-3 a^7 z^3+6 a^5 z^3-3 a^3 z^3-7 a z^3+5 z^3 a^{-1} -a^8 z^2+2 a^6 z^2-8 a^4 z^2-14 a^2 z^2+10 z^2 a^{-2} +7 z^2-a^5 z+a^3 z+a z-z a^{-1} +2 a^4+2 a^2-2 a^{-2} -1 }[/math] |
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