K12a457
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+6 q^3-14 q^2+24 q-34+41 q^{-1} -43 q^{-2} +40 q^{-3} -31 q^{-4} +21 q^{-5} -11 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-29 t^2+60 t-75+60 t^{-1} -29 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^4+1 }[/math] |
| Determinant | 271 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-9 a^2 z^4-z^4 a^{-2} +4 z^4-2 a^6 z^2+9 a^4 z^2-9 a^2 z^2+2 z^2-2 a^6+5 a^4-3 a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^3 z^{11}+4 a z^{11}+13 a^4 z^{10}+25 a^2 z^{10}+12 z^{10}+19 a^5 z^9+31 a^3 z^9+25 a z^9+13 z^9 a^{-1} +17 a^6 z^8-a^4 z^8-42 a^2 z^8+6 z^8 a^{-2} -18 z^8+10 a^7 z^7-29 a^5 z^7-95 a^3 z^7-91 a z^7-34 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-28 a^6 z^6-43 a^4 z^6-12 a^2 z^6-13 z^6 a^{-2} -14 z^6+a^9 z^5-12 a^7 z^5+17 a^5 z^5+84 a^3 z^5+79 a z^5+24 z^5 a^{-1} -z^5 a^{-3} -3 a^8 z^4+26 a^6 z^4+52 a^4 z^4+38 a^2 z^4+6 z^4 a^{-2} +21 z^4-a^9 z^3+8 a^7 z^3-a^5 z^3-31 a^3 z^3-23 a z^3-2 z^3 a^{-1} -11 a^6 z^2-25 a^4 z^2-18 a^2 z^2+2 z^2 a^{-2} -2 z^2-2 a^7 z-a^5 z+3 a^3 z+a z-z a^{-1} +2 a^6+5 a^4+3 a^2- a^{-2} }[/math] |
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