K12a455
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-12 q^2+21 q-29+36 q^{-1} -38 q^{-2} +35 q^{-3} -28 q^{-4} +19 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-27 t^2+52 t-63+52 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^4+1 }[/math] |
| Determinant | 239 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-8 a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+7 a^4 z^2-8 a^2 z^2-z^2 a^{-2} +4 z^2-a^6+3 a^4-3 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+10 a^4 z^{10}+19 a^2 z^{10}+9 z^{10}+15 a^5 z^9+25 a^3 z^9+20 a z^9+10 z^9 a^{-1} +14 a^6 z^8+a^4 z^8-30 a^2 z^8+5 z^8 a^{-2} -12 z^8+9 a^7 z^7-21 a^5 z^7-77 a^3 z^7-75 a z^7-27 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-21 a^6 z^6-37 a^4 z^6-19 a^2 z^6-13 z^6 a^{-2} -20 z^6+a^9 z^5-11 a^7 z^5+11 a^5 z^5+72 a^3 z^5+71 a z^5+20 z^5 a^{-1} -2 z^5 a^{-3} -4 a^8 z^4+16 a^6 z^4+44 a^4 z^4+46 a^2 z^4+10 z^4 a^{-2} +32 z^4-a^9 z^3+6 a^7 z^3-2 a^5 z^3-29 a^3 z^3-26 a z^3-5 z^3 a^{-1} +z^3 a^{-3} +a^8 z^2-6 a^6 z^2-20 a^4 z^2-22 a^2 z^2-3 z^2 a^{-2} -12 z^2-a^7 z+4 a^3 z+4 a z+z a^{-1} +a^6+3 a^4+3 a^2+2 }[/math] |
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