K12a818
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+10 q^5-18 q^4+25 q^3-29 q^2+31 q-28+22 q^{-1} -15 q^{-2} +8 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-23 t^2+42 t-49+42 t^{-1} -23 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-z^4-3 z^2+1 }[/math] |
| Determinant | 195 |
| 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^4-12 z^4 a^{-2} +3 z^4 a^{-4} +11 z^4+a^4 z^2-8 a^2 z^2-14 z^2 a^{-2} +4 z^2 a^{-4} +14 z^2+2 a^4-5 a^2-5 a^{-2} +2 a^{-4} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+9 z^{10} a^{-2} +13 z^{10}+3 a^3 z^9+7 a z^9+23 z^9 a^{-1} +19 z^9 a^{-3} +a^4 z^8-11 a^2 z^8+7 z^8 a^{-2} +23 z^8 a^{-4} -28 z^8-13 a^3 z^7-46 a z^7-82 z^7 a^{-1} -31 z^7 a^{-3} +18 z^7 a^{-5} -5 a^4 z^6-a^2 z^6-74 z^6 a^{-2} -43 z^6 a^{-4} +10 z^6 a^{-6} -17 z^6+20 a^3 z^5+62 a z^5+69 z^5 a^{-1} -z^5 a^{-3} -24 z^5 a^{-5} +4 z^5 a^{-7} +9 a^4 z^4+25 a^2 z^4+80 z^4 a^{-2} +27 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +62 z^4-13 a^3 z^3-27 a z^3-15 z^3 a^{-1} +11 z^3 a^{-3} +12 z^3 a^{-5} -7 a^4 z^2-22 a^2 z^2-34 z^2 a^{-2} -10 z^2 a^{-4} +2 z^2 a^{-6} -37 z^2+3 a^3 z+4 a z-3 z a^{-3} -2 z a^{-5} +2 a^4+5 a^2+5 a^{-2} +2 a^{-4} +7 }[/math] |
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