K12a645
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-22 q^6+32 q^5-39 q^4+42 q^3-38 q^2+31 q-21+11 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-30 t^2+54 t-65+54 t^{-1} -30 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-4 z^4+z^2+1 }[/math] |
| Determinant | 259 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +z^6-8 z^4 a^{-2} -z^4 a^{-4} +2 z^4 a^{-6} +3 z^4-9 z^2 a^{-2} +6 z^2 a^{-4} +4 z^2-4 a^{-2} +5 a^{-4} -2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +19 z^{10} a^{-4} +10 z^{10} a^{-6} +12 z^9 a^{-1} +23 z^9 a^{-3} +25 z^9 a^{-5} +14 z^9 a^{-7} +z^8 a^{-2} -19 z^8 a^{-4} +11 z^8 a^{-8} +9 z^8+4 a z^7-19 z^7 a^{-1} -57 z^7 a^{-3} -61 z^7 a^{-5} -22 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-31 z^6 a^{-2} -23 z^6 a^{-4} -31 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -17 z^6-7 a z^5+10 z^5 a^{-1} +42 z^5 a^{-3} +39 z^5 a^{-5} +6 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+37 z^4 a^{-2} +38 z^4 a^{-4} +29 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +14 z^4+4 a z^3-2 z^3 a^{-1} -11 z^3 a^{-3} -4 z^3 a^{-5} +4 z^3 a^{-7} +3 z^3 a^{-9} +a^2 z^2-20 z^2 a^{-2} -20 z^2 a^{-4} -10 z^2 a^{-6} -2 z^2 a^{-8} -7 z^2-a z-z a^{-1} -2 z a^{-5} -2 z a^{-7} +4 a^{-2} +5 a^{-4} +2 a^{-6} +2 }[/math] |
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