K12a857
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+10 q-18+28 q^{-1} -35 q^{-2} +38 q^{-3} -36 q^{-4} +30 q^{-5} -21 q^{-6} +12 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-29 t^2+49 t-57+49 t^{-1} -29 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-3 z^4+1 }[/math] |
| Determinant | 239 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-3 a^4 z^6-4 a^2 z^6+z^6+2 a^6 z^4-a^4 z^4-7 a^2 z^4+3 z^4+4 a^4 z^2-7 a^2 z^2+3 z^2-a^6+3 a^4-3 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+9 a^6 z^{10}+18 a^4 z^{10}+9 a^2 z^{10}+13 a^7 z^9+19 a^5 z^9+18 a^3 z^9+12 a z^9+11 a^8 z^8-a^6 z^8-30 a^4 z^8-9 a^2 z^8+9 z^8+5 a^9 z^7-20 a^7 z^7-50 a^5 z^7-58 a^3 z^7-29 a z^7+4 z^7 a^{-1} +a^{10} z^6-21 a^8 z^6-24 a^6 z^6+8 a^4 z^6-13 a^2 z^6+z^6 a^{-2} -22 z^6-8 a^9 z^5+3 a^7 z^5+39 a^5 z^5+65 a^3 z^5+29 a z^5-8 z^5 a^{-1} -a^{10} z^4+11 a^8 z^4+17 a^6 z^4+16 a^4 z^4+32 a^2 z^4-2 z^4 a^{-2} +19 z^4+3 a^9 z^3+2 a^7 z^3-15 a^5 z^3-28 a^3 z^3-12 a z^3+2 z^3 a^{-1} -a^8 z^2-5 a^6 z^2-14 a^4 z^2-18 a^2 z^2-8 z^2+2 a^5 z+4 a^3 z+2 a z+a^6+3 a^4+3 a^2+2 }[/math] |
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