K12n378
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^2+6 q-10+15 q^{-1} -17 q^{-2} +18 q^{-3} -16 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-12 t^2+24 t-29+24 t^{-1} -12 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+6 z^4+3 z^2+1 }[/math] |
| Determinant | 107 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+2 z^4 a^4+z^2 a^4+2 z^6 a^2+7 z^4 a^2+8 z^2 a^2+3 a^2-2 z^4-4 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+4 a^5 z^9+6 a^3 z^9+2 a z^9+6 a^6 z^8+10 a^4 z^8+5 a^2 z^8+z^8+5 a^7 z^7-4 a^3 z^7+a z^7+3 a^8 z^6-9 a^6 z^6-23 a^4 z^6-7 a^2 z^6+4 z^6+a^9 z^5-7 a^7 z^5-8 a^5 z^5-8 a^3 z^5-5 a z^5+3 z^5 a^{-1} -5 a^8 z^4+8 a^6 z^4+19 a^4 z^4-6 a^2 z^4-12 z^4-2 a^9 z^3+3 a^7 z^3+9 a^5 z^3+8 a^3 z^3-a z^3-5 z^3 a^{-1} +2 a^8 z^2-5 a^6 z^2-5 a^4 z^2+9 a^2 z^2+7 z^2+a^9 z-a^7 z-3 a^5 z-a^3 z+a z+z a^{-1} +a^6-3 a^2-1 }[/math] |
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