K12n827
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^7-6 q^6+11 q^5-16 q^4+19 q^3-20 q^2+18 q-13+9 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-14 t^2+25 t-29+25 t^{-1} -14 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-4 z^4-2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +z^6-9 z^4 a^{-2} +2 z^4 a^{-4} +3 z^4-6 z^2 a^{-2} +z^2 a^{-6} +3 z^2- a^{-2} - a^{-4} + a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +6 z^9 a^{-1} +10 z^9 a^{-3} +4 z^9 a^{-5} +8 z^8 a^{-2} +4 z^8 a^{-4} +3 z^8 a^{-6} +7 z^8+4 a z^7-10 z^7 a^{-1} -19 z^7 a^{-3} -4 z^7 a^{-5} +z^7 a^{-7} +a^2 z^6-26 z^6 a^{-2} -7 z^6 a^{-4} +z^6 a^{-6} -17 z^6-9 a z^5+z^5 a^{-1} +12 z^5 a^{-3} +7 z^5 a^{-5} +5 z^5 a^{-7} -2 a^2 z^4+19 z^4 a^{-2} -3 z^4 a^{-6} +3 z^4 a^{-8} +11 z^4+4 a z^3-3 z^3 a^{-3} -6 z^3 a^{-5} -7 z^3 a^{-7} +a^2 z^2-6 z^2 a^{-2} +4 z^2 a^{-4} +2 z^2 a^{-6} -3 z^2 a^{-8} -4 z^2+2 z a^{-5} +2 z a^{-7} + a^{-2} - a^{-4} - a^{-6} +2 }[/math] |
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