K13a1033
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Polynomial invariants
| Jones polynomial | Data:K13a1033/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+13 t^3-40 t^2+76 t-93+76 t^{-1} -40 t^{-2} +13 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1033/Conway Polynomial |
| Determinant | 355 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-4 a^4 z^6-2 a^2 z^6+2 z^6+3 a^6 z^4-9 a^4 z^4-z^4 a^{-2} +5 z^4+4 a^6 z^2-9 a^4 z^2+3 a^2 z^2-2 z^2 a^{-2} +5 z^2+a^6-3 a^4+2 a^2- a^{-2} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^{12}+2 a^2 z^{12}+8 a^5 z^{11}+15 a^3 z^{11}+7 a z^{11}+14 a^6 z^{10}+28 a^4 z^{10}+24 a^2 z^{10}+10 z^{10}+14 a^7 z^9+14 a^5 z^9-2 a^3 z^9+6 a z^9+8 z^9 a^{-1} +9 a^8 z^8-15 a^6 z^8-61 a^4 z^8-56 a^2 z^8+4 z^8 a^{-2} -15 z^8+4 a^9 z^7-24 a^7 z^7-57 a^5 z^7-52 a^3 z^7-42 a z^7-18 z^7 a^{-1} +z^7 a^{-3} +a^{10} z^6-15 a^8 z^6-a^6 z^6+41 a^4 z^6+33 a^2 z^6-11 z^6 a^{-2} -4 z^6-7 a^9 z^5+20 a^7 z^5+59 a^5 z^5+57 a^3 z^5+40 a z^5+12 z^5 a^{-1} -3 z^5 a^{-3} -2 a^{10} z^4+10 a^8 z^4+8 a^6 z^4-16 a^4 z^4-7 a^2 z^4+11 z^4 a^{-2} +16 z^4+4 a^9 z^3-8 a^7 z^3-26 a^5 z^3-26 a^3 z^3-16 a z^3-z^3 a^{-1} +3 z^3 a^{-3} +a^{10} z^2-3 a^8 z^2-a^6 z^2+10 a^4 z^2+2 a^2 z^2-5 z^2 a^{-2} -10 z^2-a^9 z+5 a^5 z+6 a^3 z+2 a z-z a^{-1} -z a^{-3} -a^6-3 a^4-2 a^2+ a^{-2} +2 }[/math] |
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