K12n532
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-6 q^3+12 q^2-17 q+20-21 q^{-1} +19 q^{-2} -14 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+11 t^2-29 t+41-29 t^{-1} +11 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-z^4-3 z^2+1 }[/math] |
| Determinant | 125 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6+a^4 z^4-2 a^2 z^4+z^4 a^{-2} -z^4+a^4 z^2-3 a^2 z^2-z^2 a^{-2} +a^4-a^2- a^{-2} + a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^2 z^{10}+3 z^{10}+8 a^3 z^9+14 a z^9+6 z^9 a^{-1} +8 a^4 z^8+6 a^2 z^8+4 z^8 a^{-2} +2 z^8+4 a^5 z^7-20 a^3 z^7-39 a z^7-14 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-22 a^4 z^6-33 a^2 z^6-4 z^6 a^{-2} -14 z^6-9 a^5 z^5+16 a^3 z^5+44 a z^5+24 z^5 a^{-1} +5 z^5 a^{-3} -2 a^6 z^4+18 a^4 z^4+36 a^2 z^4+7 z^4 a^{-2} +3 z^4 a^{-4} +20 z^4+3 a^5 z^3-8 a^3 z^3-21 a z^3-17 z^3 a^{-1} -7 z^3 a^{-3} -7 a^4 z^2-13 a^2 z^2-7 z^2 a^{-2} -4 z^2 a^{-4} -9 z^2+2 a^3 z+3 a z+3 z a^{-1} +2 z a^{-3} +a^4+a^2+ a^{-2} + a^{-4} +1 }[/math] |
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