# 10 133 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 133's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 133 at Knotilus!

### Knot presentations

 Planar diagram presentation X1425 X3849 X14,9,15,10 X5,13,6,12 X13,7,14,6 X18,11,19,12 X20,15,1,16 X16,19,17,20 X10,17,11,18 X7283 Gauss code -1, 10, -2, 1, -4, 5, -10, 2, 3, -9, 6, 4, -5, -3, 7, -8, 9, -6, 8, -7 Dowker-Thistlethwaite code 4 8 12 2 -14 -18 6 -20 -10 -16 Conway Notation [23,21,2-]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 1 3-genus 2 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-11] Hyperbolic Volume 7.7983 A-Polynomial See Data:10 133/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $2$ Rasmussen s-Invariant -2

### Polynomial invariants

 Alexander polynomial $-t^2+5 t-7+5 t^{-1} - t^{-2}$ Conway polynomial $-z^4+z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 19, -2 } Jones polynomial $q^{-1} - q^{-2} +3 q^{-3} -3 q^{-4} +3 q^{-5} -3 q^{-6} +2 q^{-7} -2 q^{-8} + q^{-9}$ HOMFLY-PT polynomial (db, data sources) $z^2 a^8+a^8-z^4 a^6-3 z^2 a^6-3 a^6+2 z^2 a^4+2 a^4+z^2 a^2+a^2$ Kauffman polynomial (db, data sources) $z^6 a^{10}-4 z^4 a^{10}+3 z^2 a^{10}+2 z^7 a^9-9 z^5 a^9+10 z^3 a^9-3 z a^9+z^8 a^8-3 z^6 a^8+z^2 a^8+a^8+3 z^7 a^7-13 z^5 a^7+16 z^3 a^7-7 z a^7+z^8 a^6-4 z^6 a^6+6 z^4 a^6-6 z^2 a^6+3 a^6+z^7 a^5-4 z^5 a^5+7 z^3 a^5-4 z a^5+2 z^4 a^4-3 z^2 a^4+2 a^4+z^3 a^3+z^2 a^2-a^2$ The A2 invariant $q^{28}-2 q^{20}-q^{18}-q^{16}+q^{12}+q^{10}+2 q^8+q^6+q^2$ The G2 invariant $q^{142}-q^{140}+2 q^{138}-3 q^{136}+q^{134}-q^{132}-3 q^{130}+6 q^{128}-6 q^{126}+4 q^{124}-q^{122}-2 q^{120}+5 q^{118}-4 q^{116}+2 q^{114}+3 q^{112}-3 q^{110}+4 q^{108}+q^{106}-3 q^{104}+8 q^{102}-6 q^{100}+3 q^{98}+q^{96}-4 q^{94}+5 q^{92}-6 q^{90}+3 q^{88}-4 q^{86}-q^{82}-5 q^{80}+q^{78}-4 q^{76}-3 q^{70}+q^{66}-4 q^{64}+6 q^{62}-5 q^{60}+2 q^{58}+4 q^{56}-5 q^{54}+7 q^{52}-2 q^{50}+q^{48}+3 q^{46}-2 q^{44}+q^{42}+2 q^{40}+2 q^{36}+q^{34}-q^{32}+2 q^{30}-q^{28}+q^{26}+q^{24}-q^{22}+2 q^{20}+q^{14}+q^{10}$