# 10 119 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 119's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 119 at Knotilus!

### Knot presentations

 Planar diagram presentation X1627 X7,18,8,19 X3948 X17,3,18,2 X5,15,6,14 X9,17,10,16 X15,11,16,10 X11,5,12,4 X13,20,14,1 X19,12,20,13 Gauss code -1, 4, -3, 8, -5, 1, -2, 3, -6, 7, -8, 10, -9, 5, -7, 6, -4, 2, -10, 9 Dowker-Thistlethwaite code 6 8 14 18 16 4 20 10 2 12 Conway Notation [8*2:.20]

### Three dimensional invariants

 Symmetry type Chiral Unknotting number 1 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-5][-7] Hyperbolic Volume 15.9387 A-Polynomial See Data:10 119/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $3$ Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial $-2 t^3+10 t^2-23 t+31-23 t^{-1} +10 t^{-2} -2 t^{-3}$ Conway polynomial $-2 z^6-2 z^4-z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 101, 0 } Jones polynomial $q^6-4 q^5+8 q^4-12 q^3+16 q^2-17 q+16-13 q^{-1} +9 q^{-2} -4 q^{-3} + q^{-4}$ HOMFLY-PT polynomial (db, data sources) $-z^6 a^{-2} -z^6+a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -2 z^4+a^2 z^2-z^2 a^{-2} +z^2 a^{-4} -2 z^2+a^2+ a^{-2} -1$ Kauffman polynomial (db, data sources) $3 z^9 a^{-1} +3 z^9 a^{-3} +15 z^8 a^{-2} +6 z^8 a^{-4} +9 z^8+12 a z^7+13 z^7 a^{-1} +5 z^7 a^{-3} +4 z^7 a^{-5} +9 a^2 z^6-31 z^6 a^{-2} -14 z^6 a^{-4} +z^6 a^{-6} -7 z^6+4 a^3 z^5-17 a z^5-37 z^5 a^{-1} -26 z^5 a^{-3} -10 z^5 a^{-5} +a^4 z^4-9 a^2 z^4+13 z^4 a^{-2} +8 z^4 a^{-4} -2 z^4 a^{-6} -7 z^4-a^3 z^3+9 a z^3+22 z^3 a^{-1} +19 z^3 a^{-3} +7 z^3 a^{-5} +4 a^2 z^2+z^2 a^{-2} +z^2 a^{-6} +6 z^2-2 a z-4 z a^{-1} -3 z a^{-3} -z a^{-5} -a^2- a^{-2} -1$ The A2 invariant $q^{12}-2 q^{10}+2 q^8+2 q^6-3 q^4+3 q^2-3+ q^{-2} + q^{-4} - q^{-6} +4 q^{-8} -3 q^{-10} + q^{-12} + q^{-14} -2 q^{-16} + q^{-18}$ The G2 invariant $q^{66}-3 q^{64}+6 q^{62}-10 q^{60}+11 q^{58}-10 q^{56}+4 q^{54}+14 q^{52}-35 q^{50}+60 q^{48}-78 q^{46}+71 q^{44}-44 q^{42}-17 q^{40}+105 q^{38}-184 q^{36}+238 q^{34}-223 q^{32}+127 q^{30}+33 q^{28}-222 q^{26}+371 q^{24}-410 q^{22}+305 q^{20}-82 q^{18}-176 q^{16}+370 q^{14}-400 q^{12}+264 q^{10}-15 q^8-242 q^6+363 q^4-299 q^2+59+250 q^{-2} -475 q^{-4} +516 q^{-6} -332 q^{-8} - q^{-10} +350 q^{-12} -598 q^{-14} +642 q^{-16} -473 q^{-18} +155 q^{-20} +204 q^{-22} -467 q^{-24} +561 q^{-26} -441 q^{-28} +178 q^{-30} +115 q^{-32} -337 q^{-34} +382 q^{-36} -246 q^{-38} -7 q^{-40} +274 q^{-42} -413 q^{-44} +359 q^{-46} -130 q^{-48} -174 q^{-50} +415 q^{-52} -496 q^{-54} +387 q^{-56} -150 q^{-58} -116 q^{-60} +311 q^{-62} -370 q^{-64} +302 q^{-66} -149 q^{-68} -7 q^{-70} +108 q^{-72} -148 q^{-74} +125 q^{-76} -73 q^{-78} +27 q^{-80} +8 q^{-82} -22 q^{-84} +21 q^{-86} -16 q^{-88} +8 q^{-90} -3 q^{-92} + q^{-94}$