K13a505
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Polynomial invariants
| Jones polynomial | Data:K13a505/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-33 t^2+58 t-69+58 t^{-1} -33 t^{-2} +12 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a505/Conway Polynomial |
| Determinant | 279 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-4 a^4 z^6-3 a^2 z^6+2 z^6+3 a^6 z^4-8 a^4 z^4-2 a^2 z^4-z^4 a^{-2} +7 z^4+4 a^6 z^2-10 a^4 z^2+3 a^2 z^2-3 z^2 a^{-2} +8 z^2+2 a^6-6 a^4+4 a^2-2 a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{12}+a^2 z^{12}+5 a^5 z^{11}+8 a^3 z^{11}+3 a z^{11}+11 a^6 z^{10}+19 a^4 z^{10}+13 a^2 z^{10}+5 z^{10}+13 a^7 z^9+14 a^5 z^9+5 a^3 z^9+9 a z^9+5 z^9 a^{-1} +9 a^8 z^8-13 a^6 z^8-41 a^4 z^8-27 a^2 z^8+3 z^8 a^{-2} -5 z^8+4 a^9 z^7-27 a^7 z^7-57 a^5 z^7-53 a^3 z^7-41 a z^7-13 z^7 a^{-1} +z^7 a^{-3} +a^{10} z^6-17 a^8 z^6-2 a^6 z^6+28 a^4 z^6+9 a^2 z^6-10 z^6 a^{-2} -13 z^6-7 a^9 z^5+27 a^7 z^5+78 a^5 z^5+83 a^3 z^5+52 a z^5+9 z^5 a^{-1} -4 z^5 a^{-3} -2 a^{10} z^4+11 a^8 z^4+8 a^6 z^4-6 a^4 z^4+10 a^2 z^4+11 z^4 a^{-2} +22 z^4+3 a^9 z^3-21 a^7 z^3-58 a^5 z^3-60 a^3 z^3-32 a z^3-z^3 a^{-1} +5 z^3 a^{-3} +a^{10} z^2-4 a^8 z^2-3 a^6 z^2+7 a^4 z^2-2 a^2 z^2-6 z^2 a^{-2} -13 z^2+7 a^7 z+20 a^5 z+20 a^3 z+8 a z-z a^{-1} -2 z a^{-3} -2 a^6-6 a^4-4 a^2+2 a^{-2} +3 }[/math] |
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