L7a2 (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L7a2 at Knotilus! L7a2 is $7^2_5$ in the Rolfsen table of links.

Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $\frac{-2 u v^2+2 u v-u-v^3+2 v^2-2 v}{\sqrt{u} v^{3/2}}$ (db) Jones polynomial $-\frac{1}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{4}{q^{7/2}}+\frac{3}{q^{9/2}}-\frac{4}{q^{11/2}}+\frac{3}{q^{13/2}}-\frac{2}{q^{15/2}}+\frac{1}{q^{17/2}}$ (db) Signature -3 (db) HOMFLY-PT polynomial $-a^9 z^{-1} +3 a^7 z+3 a^7 z^{-1} -2 a^5 z^3-4 a^5 z-2 a^5 z^{-1} -a^3 z^3-a^3 z$ (db) Kauffman polynomial $a^{10} z^4-2 a^{10} z^2+a^{10}+2 a^9 z^5-4 a^9 z^3+2 a^9 z-a^9 z^{-1} +a^8 z^6+2 a^8 z^4-7 a^8 z^2+3 a^8+5 a^7 z^5-10 a^7 z^3+8 a^7 z-3 a^7 z^{-1} +a^6 z^6+3 a^6 z^4-6 a^6 z^2+3 a^6+3 a^5 z^5-5 a^5 z^3+5 a^5 z-2 a^5 z^{-1} +2 a^4 z^4-a^4 z^2+a^3 z^3-a^3 z$ (db)

Khovanov Homology

The coefficients of the monomials $t^rq^j$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over $r$).
 \ r \ j \
-7-6-5-4-3-2-10χ
-2       11
-4      21-1
-6     2  2
-8    12  1
-10   32   1
-12  12    1
-14 12     -1
-16 1      1
-181       -1
Integral Khovanov Homology $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=-4$ $i=-2$ $r=-7$ ${\mathbb Z}$ $r=-6$ ${\mathbb Z}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-5$ ${\mathbb Z}^{2}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-4$ ${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{3}$ $r=-3$ ${\mathbb Z}^{2}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-2$ ${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ $r=-1$ ${\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ $r=0$ ${\mathbb Z}$ ${\mathbb Z}$

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory. See A Sample KnotTheory Session.