K12a488
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+9 q^5-15 q^4+22 q^3-26 q^2+27 q-25+20 q^{-1} -14 q^{-2} +8 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-22 t^2+37 t-41+37 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-4 z^2+1 }[/math] |
| Determinant | 175 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +3 z^6-3 a^2 z^4-11 z^4 a^{-2} +3 z^4 a^{-4} +11 z^4+a^4 z^2-8 a^2 z^2-12 z^2 a^{-2} +3 z^2 a^{-4} +12 z^2+2 a^4-4 a^2-4 a^{-2} +2 a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+8 z^{10} a^{-2} +12 z^{10}+3 a^3 z^9+5 a z^9+17 z^9 a^{-1} +15 z^9 a^{-3} +a^4 z^8-12 a^2 z^8-z^8 a^{-2} +17 z^8 a^{-4} -31 z^8-13 a^3 z^7-40 a z^7-68 z^7 a^{-1} -27 z^7 a^{-3} +14 z^7 a^{-5} -5 a^4 z^6+2 a^2 z^6-45 z^6 a^{-2} -29 z^6 a^{-4} +9 z^6 a^{-6} +19 a^3 z^5+53 a z^5+62 z^5 a^{-1} +7 z^5 a^{-3} -17 z^5 a^{-5} +4 z^5 a^{-7} +9 a^4 z^4+19 a^2 z^4+51 z^4 a^{-2} +15 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +38 z^4-11 a^3 z^3-20 a z^3-14 z^3 a^{-1} +2 z^3 a^{-3} +6 z^3 a^{-5} -z^3 a^{-7} -7 a^4 z^2-17 a^2 z^2-21 z^2 a^{-2} -6 z^2 a^{-4} +2 z^2 a^{-6} -23 z^2+2 a^3 z+a z-z a^{-1} -z a^{-3} -z a^{-5} +2 a^4+4 a^2+4 a^{-2} +2 a^{-4} +5 }[/math] |
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