K12a207
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+8 q^5-14 q^4+20 q^3-23 q^2+25 q-22+18 q^{-1} -13 q^{-2} +7 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-20 t^2+33 t-37+33 t^{-1} -20 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^4+1 }[/math] |
| Determinant | 159 |
| 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^4-10 z^4 a^{-2} +3 z^4 a^{-4} +12 z^4+a^4 z^2-9 a^2 z^2-9 z^2 a^{-2} +2 z^2 a^{-4} +15 z^2+2 a^4-6 a^2-2 a^{-2} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+5 z^{10} a^{-2} +8 z^{10}+3 a^3 z^9+10 a z^9+18 z^9 a^{-1} +11 z^9 a^{-3} +a^4 z^8-6 a^2 z^8+11 z^8 a^{-2} +14 z^8 a^{-4} -10 z^8-14 a^3 z^7-52 a z^7-63 z^7 a^{-1} -13 z^7 a^{-3} +12 z^7 a^{-5} -5 a^4 z^6-14 a^2 z^6-67 z^6 a^{-2} -23 z^6 a^{-4} +8 z^6 a^{-6} -45 z^6+23 a^3 z^5+72 a z^5+55 z^5 a^{-1} -12 z^5 a^{-3} -14 z^5 a^{-5} +4 z^5 a^{-7} +9 a^4 z^4+41 a^2 z^4+74 z^4 a^{-2} +12 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +87 z^4-16 a^3 z^3-38 a z^3-16 z^3 a^{-1} +12 z^3 a^{-3} +4 z^3 a^{-5} -2 z^3 a^{-7} -7 a^4 z^2-30 a^2 z^2-29 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} -47 z^2+4 a^3 z+8 a z+4 z a^{-1} +2 a^4+6 a^2+2 a^{-2} +7 }[/math] |
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