K12a146
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+2 q^{-1} -3 q^{-2} +5 q^{-3} -5 q^{-4} +7 q^{-5} -7 q^{-6} +7 q^{-7} -6 q^{-8} +5 q^{-9} -4 q^{-10} +2 q^{-11} - q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-3 t^4+6 t^3-7 t^2+7 t-7+7 t^{-1} -7 t^{-2} +6 t^{-3} -3 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+7 z^8+17 z^6+19 z^4+10 z^2+1 }[/math] |
| Determinant | 55 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6 z^{10}-a^8 z^8+9 a^6 z^8-a^4 z^8-7 a^8 z^6+31 a^6 z^6-7 a^4 z^6-17 a^8 z^4+52 a^6 z^4-16 a^4 z^4-18 a^8 z^2+42 a^6 z^2-14 a^4 z^2-7 a^8+12 a^6-4 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{15}-z a^{15}+2 z^4 a^{14}-z^2 a^{14}+3 z^5 a^{13}-3 z^3 a^{13}+2 z a^{13}+3 z^6 a^{12}-3 z^4 a^{12}+z^2 a^{12}+3 z^7 a^{11}-5 z^5 a^{11}+2 z^3 a^{11}-z a^{11}+3 z^8 a^{10}-8 z^6 a^{10}+6 z^4 a^{10}-4 z^2 a^{10}+3 z^9 a^9-11 z^7 a^9+11 z^5 a^9-6 z^3 a^9+z a^9+3 z^{10} a^8-16 z^8 a^8+32 z^6 a^8-39 z^4 a^8+27 z^2 a^8-7 a^8+z^{11} a^7-z^9 a^7-17 z^7 a^7+44 z^5 a^7-38 z^3 a^7+12 z a^7+5 z^{10} a^6-33 z^8 a^6+76 z^6 a^6-83 z^4 a^6+49 z^2 a^6-12 a^6+z^{11} a^5-3 z^9 a^5-10 z^7 a^5+41 z^5 a^5-40 z^3 a^5+11 z a^5+2 z^{10} a^4-14 z^8 a^4+33 z^6 a^4-33 z^4 a^4+16 z^2 a^4-4 a^4+z^9 a^3-7 z^7 a^3+16 z^5 a^3-14 z^3 a^3+4 z a^3 }[/math] |
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