K12a348
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-20 q^3+29 q^2-34 q+36-33 q^{-1} +25 q^{-2} -17 q^{-3} +9 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+17 t^2-54 t+79-54 t^{-1} +17 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+5 z^4-4 z^2+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4+3 z^4 a^2-z^2 a^2-3 a^2-z^6+2 z^4+4 z^2+4-z^6 a^{-2} -z^4 a^{-2} -4 z^2 a^{-2} -2 a^{-2} +z^4 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+8 z^{10} a^{-2} +14 z^{10}+8 a^3 z^9+18 a z^9+23 z^9 a^{-1} +13 z^9 a^{-3} +6 a^4 z^8+a^2 z^8+3 z^8 a^{-2} +11 z^8 a^{-4} -13 z^8+3 a^5 z^7-14 a^3 z^7-51 a z^7-62 z^7 a^{-1} -23 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-11 a^4 z^6-21 a^2 z^6-38 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -24 z^6-6 a^5 z^5+15 a^3 z^5+62 a z^5+58 z^5 a^{-1} +9 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+7 a^4 z^4+31 a^2 z^4+40 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +48 z^4+3 a^5 z^3-16 a^3 z^3-43 a z^3-28 z^3 a^{-1} -2 z^3 a^{-3} +2 z^3 a^{-5} +3 a^6 z^2-2 a^4 z^2-20 a^2 z^2-16 z^2 a^{-2} -3 z^2 a^{-4} -28 z^2+8 a^3 z+14 a z+8 z a^{-1} +2 z a^{-3} -a^6+3 a^2+2 a^{-2} + a^{-4} +4 }[/math] |
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