K12a71
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+18 q^5-25 q^4+31 q^3-33 q^2+30 q-24+17 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-25 t^2+44 t-51+44 t^{-1} -25 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+3 z^4+1 }[/math] |
| Determinant | 207 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-7 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-7 z^2 a^{-2} +6 z^2 a^{-4} -2 z^2 a^{-6} +5 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +7 z^{10} a^{-4} +6 z^{10}+7 a z^9+14 z^9 a^{-1} +19 z^9 a^{-3} +12 z^9 a^{-5} +4 a^2 z^8-18 z^8 a^{-2} +7 z^8 a^{-4} +13 z^8 a^{-6} -8 z^8+a^3 z^7-21 a z^7-52 z^7 a^{-1} -51 z^7 a^{-3} -12 z^7 a^{-5} +9 z^7 a^{-7} -13 a^2 z^6-18 z^6 a^{-2} -40 z^6 a^{-4} -20 z^6 a^{-6} +4 z^6 a^{-8} -15 z^6-3 a^3 z^5+19 a z^5+51 z^5 a^{-1} +38 z^5 a^{-3} -4 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+37 z^4 a^{-2} +42 z^4 a^{-4} +15 z^4 a^{-6} -4 z^4 a^{-8} +27 z^4+2 a^3 z^3-7 a z^3-19 z^3 a^{-1} -9 z^3 a^{-3} +9 z^3 a^{-5} +7 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2-19 z^2 a^{-2} -19 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} -13 z^2+a z+3 z a^{-1} +z a^{-3} -3 z a^{-5} -2 z a^{-7} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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