# 10 71 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 71's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 71 at Knotilus!

### Knot presentations

 Planar diagram presentation X1425 X3849 X11,15,12,14 X5,13,6,12 X13,7,14,6 X9,19,10,18 X15,20,16,1 X19,16,20,17 X17,11,18,10 X7283 Gauss code -1, 10, -2, 1, -4, 5, -10, 2, -6, 9, -3, 4, -5, 3, -7, 8, -9, 6, -8, 7 Dowker-Thistlethwaite code 4 8 12 2 18 14 6 20 10 16 Conway Notation [22,21,2+]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 1 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-6] Hyperbolic Volume 13.3852 A-Polynomial See Data:10 71/A-polynomial

### Four dimensional invariants

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

### Polynomial invariants

 Alexander polynomial $-t^3+7 t^2-18 t+25-18 t^{-1} +7 t^{-2} - t^{-3}$ Conway polynomial $-z^6+z^4+z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 77, 0 } Jones polynomial $-q^5+3 q^4-6 q^3+10 q^2-12 q+13-12 q^{-1} +10 q^{-2} -6 q^{-3} +3 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $-z^6+2 a^2 z^4+2 z^4 a^{-2} -3 z^4-a^4 z^2+4 a^2 z^2+4 z^2 a^{-2} -z^2 a^{-4} -5 z^2-a^4+3 a^2+3 a^{-2} - a^{-4} -3$ Kauffman polynomial (db, data sources) $a z^9+z^9 a^{-1} +3 a^2 z^8+3 z^8 a^{-2} +6 z^8+4 a^3 z^7+8 a z^7+8 z^7 a^{-1} +4 z^7 a^{-3} +3 a^4 z^6+2 a^2 z^6+2 z^6 a^{-2} +3 z^6 a^{-4} -2 z^6+a^5 z^5-5 a^3 z^5-15 a z^5-15 z^5 a^{-1} -5 z^5 a^{-3} +z^5 a^{-5} -6 a^4 z^4-12 a^2 z^4-12 z^4 a^{-2} -6 z^4 a^{-4} -12 z^4-2 a^5 z^3+7 a z^3+7 z^3 a^{-1} -2 z^3 a^{-5} +4 a^4 z^2+10 a^2 z^2+10 z^2 a^{-2} +4 z^2 a^{-4} +12 z^2+a^5 z+a^3 z-a z-z a^{-1} +z a^{-3} +z a^{-5} -a^4-3 a^2-3 a^{-2} - a^{-4} -3$ The A2 invariant $-q^{16}+q^{12}-2 q^{10}+3 q^8+q^6-q^4+2 q^2-3+2 q^{-2} - q^{-4} + q^{-6} +3 q^{-8} -2 q^{-10} + q^{-12} - q^{-16}$ The G2 invariant $q^{80}-2 q^{78}+5 q^{76}-8 q^{74}+8 q^{72}-7 q^{70}-2 q^{68}+16 q^{66}-32 q^{64}+47 q^{62}-52 q^{60}+36 q^{58}-3 q^{56}-48 q^{54}+102 q^{52}-137 q^{50}+132 q^{48}-84 q^{46}-6 q^{44}+105 q^{42}-179 q^{40}+206 q^{38}-155 q^{36}+56 q^{34}+61 q^{32}-147 q^{30}+164 q^{28}-107 q^{26}+10 q^{24}+90 q^{22}-135 q^{20}+110 q^{18}-14 q^{16}-110 q^{14}+208 q^{12}-235 q^{10}+166 q^8-34 q^6-128 q^4+254 q^2-299+253 q^{-2} -128 q^{-4} -32 q^{-6} +166 q^{-8} -233 q^{-10} +206 q^{-12} -108 q^{-14} -12 q^{-16} +109 q^{-18} -135 q^{-20} +90 q^{-22} +10 q^{-24} -107 q^{-26} +164 q^{-28} -150 q^{-30} +63 q^{-32} +55 q^{-34} -156 q^{-36} +206 q^{-38} -180 q^{-40} +106 q^{-42} -6 q^{-44} -84 q^{-46} +132 q^{-48} -136 q^{-50} +102 q^{-52} -47 q^{-54} -4 q^{-56} +36 q^{-58} -51 q^{-60} +46 q^{-62} -32 q^{-64} +16 q^{-66} -2 q^{-68} -7 q^{-70} +8 q^{-72} -8 q^{-74} +5 q^{-76} -2 q^{-78} + q^{-80}$