K12a971
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-8 q^2+14 q-20+24 q^{-1} -25 q^{-2} +24 q^{-3} -19 q^{-4} +13 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-18 t^2+37 t-45+37 t^{-1} -18 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+6 z^4+z^2+1 }[/math] |
| Determinant | 163 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+2 z^4 a^4+2 z^2 a^4+a^4+2 z^6 a^2+5 z^4 a^2+4 z^2 a^2+2 a^2+z^6+z^4-2 z^2-2-z^4 a^{-2} -z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+11 a^2 z^{10}+5 z^{10}+9 a^5 z^9+8 a^3 z^9+5 a z^9+6 z^9 a^{-1} +9 a^6 z^8-9 a^4 z^8-33 a^2 z^8+4 z^8 a^{-2} -11 z^8+6 a^7 z^7-22 a^5 z^7-35 a^3 z^7-27 a z^7-19 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-23 a^6 z^6+44 a^2 z^6-14 z^6 a^{-2} +4 z^6+a^9 z^5-12 a^7 z^5+24 a^5 z^5+50 a^3 z^5+32 a z^5+16 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+27 a^6 z^4+14 a^4 z^4-37 a^2 z^4+13 z^4 a^{-2} -6 z^4-2 a^9 z^3+8 a^7 z^3-4 a^5 z^3-31 a^3 z^3-23 a z^3-4 z^3 a^{-1} +2 z^3 a^{-3} -10 a^6 z^2-7 a^4 z^2+12 a^2 z^2-z^2 a^{-2} +8 z^2-2 a^7 z+6 a^3 z+5 a z+z a^{-1} +a^6+a^4-2 a^2- a^{-2} -2 }[/math] |
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