K12n412
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-6+10 q^{-1} -11 q^{-2} +13 q^{-3} -12 q^{-4} +9 q^{-5} -6 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-8 t^2+17 t-21+17 t^{-1} -8 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 75 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+3 z^4 a^4+3 z^2 a^4+z^6 a^2+3 z^4 a^2+4 z^2 a^2+3 a^2-z^4-2 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+3 a^5 z^9+4 a^3 z^9+a z^9+5 a^6 z^8+2 a^4 z^8-3 a^2 z^8+5 a^7 z^7-4 a^5 z^7-12 a^3 z^7-3 a z^7+3 a^8 z^6-12 a^6 z^6-8 a^4 z^6+10 a^2 z^6+3 z^6+a^9 z^5-12 a^7 z^5-a^5 z^5+21 a^3 z^5+10 a z^5+z^5 a^{-1} -6 a^8 z^4+12 a^6 z^4+13 a^4 z^4-12 a^2 z^4-7 z^4-2 a^9 z^3+9 a^7 z^3+8 a^5 z^3-15 a^3 z^3-15 a z^3-3 z^3 a^{-1} +a^8 z^2-5 a^6 z^2-5 a^4 z^2+5 a^2 z^2+4 z^2-3 a^7 z-2 a^5 z+4 a^3 z+5 a z+2 z a^{-1} +a^6-3 a^2-1 }[/math] |
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