K12n39
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^3+6 q^2-9 q+13-15 q^{-1} +15 q^{-2} -13 q^{-3} +10 q^{-4} -6 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+8 t^2-22 t+31-22 t^{-1} +8 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 93 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+4 z^2 a^4+3 a^4-z^6 a^2-3 z^4 a^2-6 z^2 a^2-4 a^2+3 z^4+6 z^2+4-2 z^2 a^{-2} - a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+3 a^5 z^9+7 a^3 z^9+4 a z^9+3 a^6 z^8+7 a^4 z^8+10 a^2 z^8+6 z^8+a^7 z^7-7 a^5 z^7-15 a^3 z^7-3 a z^7+4 z^7 a^{-1} -12 a^6 z^6-34 a^4 z^6-36 a^2 z^6+z^6 a^{-2} -13 z^6-4 a^7 z^5-3 a^5 z^5-2 a^3 z^5-6 a z^5-3 z^5 a^{-1} +15 a^6 z^4+39 a^4 z^4+38 a^2 z^4+6 z^4 a^{-2} +20 z^4+5 a^7 z^3+11 a^5 z^3+11 a^3 z^3+6 a z^3+4 z^3 a^{-1} +3 z^3 a^{-3} -7 a^6 z^2-17 a^4 z^2-20 a^2 z^2-6 z^2 a^{-2} -16 z^2-2 a^7 z-4 a^5 z-3 a^3 z-2 a z-2 z a^{-1} -z a^{-3} +a^6+3 a^4+4 a^2+ a^{-2} +4 }[/math] |
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