K12n712
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^2+6 q-10+16 q^{-1} -19 q^{-2} +20 q^{-3} -18 q^{-4} +14 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-13 t^2+27 t-33+27 t^{-1} -13 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+5 z^4+2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-z^2 a^6+z^6 a^4+z^4 a^4-2 z^2 a^4-2 a^4+2 z^6 a^2+7 z^4 a^2+9 z^2 a^2+4 a^2-2 z^4-4 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^{10}+2 a^2 z^{10}+6 a^5 z^9+9 a^3 z^9+3 a z^9+9 a^6 z^8+7 a^4 z^8-a^2 z^8+z^8+8 a^7 z^7-4 a^5 z^7-18 a^3 z^7-6 a z^7+4 a^8 z^6-14 a^6 z^6-14 a^4 z^6+8 a^2 z^6+4 z^6+a^9 z^5-13 a^7 z^5-3 a^5 z^5+20 a^3 z^5+12 a z^5+3 z^5 a^{-1} -5 a^8 z^4+7 a^6 z^4+4 a^4 z^4-21 a^2 z^4-13 z^4-a^9 z^3+6 a^7 z^3+a^5 z^3-15 a^3 z^3-15 a z^3-6 z^3 a^{-1} +a^8 z^2-2 a^6 z^2+4 a^4 z^2+16 a^2 z^2+9 z^2-a^7 z+a^5 z+5 a^3 z+5 a z+2 z a^{-1} -2 a^4-4 a^2-1 }[/math] |
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