K12a470
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-20 q^6+29 q^5-36 q^4+40 q^3-37 q^2+31 q-21+12 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-27 t^2+54 t-67+54 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^4+2 z^2+1 }[/math] |
| Determinant | 247 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +3 z^6 a^{-4} +z^6-7 z^4 a^{-2} +9 z^4 a^{-4} -3 z^4 a^{-6} +2 z^4-4 z^2 a^{-2} +10 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +z^2+4 a^{-4} -4 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +8 z^{10} a^{-2} +15 z^{10} a^{-4} +7 z^{10} a^{-6} +13 z^9 a^{-1} +27 z^9 a^{-3} +24 z^9 a^{-5} +10 z^9 a^{-7} +9 z^8 a^{-2} -3 z^8 a^{-4} +7 z^8 a^{-6} +8 z^8 a^{-8} +11 z^8+5 a z^7-19 z^7 a^{-1} -61 z^7 a^{-3} -53 z^7 a^{-5} -12 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-48 z^6 a^{-2} -48 z^6 a^{-4} -37 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} -21 z^6-8 a z^5+3 z^5 a^{-1} +37 z^5 a^{-3} +32 z^5 a^{-5} -2 z^5 a^{-7} -8 z^5 a^{-9} -a^2 z^4+42 z^4 a^{-2} +54 z^4 a^{-4} +37 z^4 a^{-6} +9 z^4 a^{-8} -2 z^4 a^{-10} +13 z^4+3 a z^3+3 z^3 a^{-1} -5 z^3 a^{-3} -z^3 a^{-5} +10 z^3 a^{-7} +6 z^3 a^{-9} -12 z^2 a^{-2} -22 z^2 a^{-4} -17 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} -3 z^2-4 z a^{-5} -6 z a^{-7} -2 z a^{-9} +4 a^{-4} +4 a^{-6} + a^{-8} }[/math] |
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