# 10 104 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 104's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 104 at Knotilus!

### Knot presentations

 Planar diagram presentation X6271 X16,4,17,3 X18,9,19,10 X14,7,15,8 X20,13,1,14 X8,17,9,18 X10,19,11,20 X12,6,13,5 X4,12,5,11 X2,16,3,15 Gauss code 1, -10, 2, -9, 8, -1, 4, -6, 3, -7, 9, -8, 5, -4, 10, -2, 6, -3, 7, -5 Dowker-Thistlethwaite code 6 16 12 14 18 4 20 2 8 10 Conway Notation [3:20:20]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 1 3-genus 4 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-6] Hyperbolic Volume 14.1071 A-Polynomial See Data:10 104/A-polynomial

### Four dimensional invariants

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

### Polynomial invariants

 Alexander polynomial $t^4-4 t^3+9 t^2-15 t+19-15 t^{-1} +9 t^{-2} -4 t^{-3} + t^{-4}$ Conway polynomial $z^8+4 z^6+5 z^4+z^2+1$ 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) $z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-4 z^4 a^{-2} +13 z^4-5 a^2 z^2-5 z^2 a^{-2} +11 z^2-a^2- a^{-2} +3$ Kauffman polynomial (db, data sources) $2 a z^9+2 z^9 a^{-1} +4 a^2 z^8+5 z^8 a^{-2} +9 z^8+4 a^3 z^7+2 a z^7+3 z^7 a^{-1} +5 z^7 a^{-3} +3 a^4 z^6-5 a^2 z^6-11 z^6 a^{-2} +3 z^6 a^{-4} -22 z^6+a^5 z^5-5 a^3 z^5-6 a z^5-12 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} -6 a^4 z^4+3 a^2 z^4+12 z^4 a^{-2} -6 z^4 a^{-4} +27 z^4-2 a^5 z^3-a^3 z^3+4 a z^3+13 z^3 a^{-1} +8 z^3 a^{-3} -2 z^3 a^{-5} +3 a^4 z^2-4 a^2 z^2-6 z^2 a^{-2} +2 z^2 a^{-4} -15 z^2+a^5 z+a^3 z-2 a z-4 z a^{-1} -2 z a^{-3} +a^2+ a^{-2} +3$ The A2 invariant $-q^{14}+q^{12}-2 q^{10}+2 q^8+q^6-q^4+3 q^2-3+3 q^{-2} - q^{-4} + q^{-6} +2 q^{-8} -2 q^{-10} + q^{-12} - q^{-14}$ The G2 invariant $q^{80}-2 q^{78}+5 q^{76}-8 q^{74}+8 q^{72}-6 q^{70}-2 q^{68}+16 q^{66}-29 q^{64}+41 q^{62}-43 q^{60}+30 q^{58}-6 q^{56}-36 q^{54}+82 q^{52}-118 q^{50}+121 q^{48}-87 q^{46}+9 q^{44}+85 q^{42}-164 q^{40}+201 q^{38}-162 q^{36}+66 q^{34}+57 q^{32}-157 q^{30}+181 q^{28}-122 q^{26}+15 q^{24}+99 q^{22}-156 q^{20}+131 q^{18}-27 q^{16}-104 q^{14}+206 q^{12}-236 q^{10}+168 q^8-34 q^6-123 q^4+244 q^2-286+243 q^{-2} -119 q^{-4} -35 q^{-6} +168 q^{-8} -234 q^{-10} +212 q^{-12} -111 q^{-14} -17 q^{-16} +126 q^{-18} -158 q^{-20} +111 q^{-22} - q^{-24} -113 q^{-26} +180 q^{-28} -166 q^{-30} +68 q^{-32} +57 q^{-34} -166 q^{-36} +212 q^{-38} -177 q^{-40} +91 q^{-42} +12 q^{-44} -99 q^{-46} +137 q^{-48} -128 q^{-50} +84 q^{-52} -29 q^{-54} -16 q^{-56} +40 q^{-58} -47 q^{-60} +40 q^{-62} -25 q^{-64} +12 q^{-66} + q^{-68} -7 q^{-70} +7 q^{-72} -7 q^{-74} +4 q^{-76} -2 q^{-78} + q^{-80}$