K12n632
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+11 q-17+23 q^{-1} -24 q^{-2} +24 q^{-3} -20 q^{-4} +13 q^{-5} -7 q^{-6} +2 q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-19 t^2+30 t-33+30 t^{-1} -19 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 147 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-z^4 a^6-4 z^2 a^6-3 a^6+2 z^6 a^4+7 z^4 a^4+7 z^2 a^4+2 a^4-z^8 a^2-4 z^6 a^2-5 z^4 a^2-2 z^2 a^2+a^2+z^6+2 z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{10}+3 a^2 z^{10}+8 a^5 z^9+17 a^3 z^9+9 a z^9+6 a^6 z^8+12 a^4 z^8+16 a^2 z^8+10 z^8+a^7 z^7-19 a^5 z^7-37 a^3 z^7-12 a z^7+5 z^7 a^{-1} -12 a^6 z^6-46 a^4 z^6-57 a^2 z^6+z^6 a^{-2} -22 z^6+7 a^7 z^5+33 a^5 z^5+27 a^3 z^5-8 a z^5-9 z^5 a^{-1} +3 a^8 z^4+24 a^6 z^4+59 a^4 z^4+51 a^2 z^4-z^4 a^{-2} +12 z^4-10 a^7 z^3-25 a^5 z^3-12 a^3 z^3+6 a z^3+3 z^3 a^{-1} -4 a^8 z^2-18 a^6 z^2-27 a^4 z^2-16 a^2 z^2-3 z^2+3 a^7 z+8 a^5 z+6 a^3 z+a z+a^8+3 a^6+2 a^4-a^2 }[/math] |
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