K12n625
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-7 q^2+11 q-14+15 q^{-1} -14 q^{-2} +12 q^{-3} -8 q^{-4} +4 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-12 t^2+18 t-19+18 t^{-1} -12 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-2 z^4-z^2+1 }[/math] |
| Determinant | 91 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+a^4 z^6-6 a^2 z^6+2 z^6+5 a^4 z^4-14 a^2 z^4-z^4 a^{-2} +8 z^4-a^6 z^2+8 a^4 z^2-15 a^2 z^2-2 z^2 a^{-2} +9 z^2-a^6+4 a^4-5 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+5 a^3 z^9+10 a z^9+5 z^9 a^{-1} +5 a^4 z^8+4 a^2 z^8+4 z^8 a^{-2} +3 z^8+2 a^5 z^7-13 a^3 z^7-33 a z^7-17 z^7 a^{-1} +z^7 a^{-3} -15 a^4 z^6-30 a^2 z^6-15 z^6 a^{-2} -30 z^6-2 a^5 z^5+12 a^3 z^5+31 a z^5+14 z^5 a^{-1} -3 z^5 a^{-3} +4 a^6 z^4+25 a^4 z^4+42 a^2 z^4+15 z^4 a^{-2} +36 z^4+a^7 z^3+6 a^5 z^3-3 a^3 z^3-13 a z^3-3 z^3 a^{-1} +2 z^3 a^{-3} -3 a^6 z^2-16 a^4 z^2-26 a^2 z^2-3 z^2 a^{-2} -16 z^2-a^7 z-2 a^5 z+a z+a^6+4 a^4+5 a^2+3 }[/math] |
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