Does anyone know what legume is the best at nitrogen fixing?
Nitrogen fixation is the soil BACTERIA's ability to convert the atmospheric nitrogen into a usable form for the plant to use. If the bacteria is present in the soil, they will form the relationship with the plant.
All legumes with the exception of Styphnolobium have the ability to form a symbiotic relationship with the soil bacteria in the Rhizobium, bradyrhizobium and azorhizobium family. The amount of nitrogen fixed is not dependent on the type of bean or the varitey, but is rather dependent on the population of the correct nitrogen fixing bacteria for your crop that is present in the soil.
I would not say there is any one particular bean that is the best at fixing nitrogen. Because the legume itself does not fix the nitrogen so if; let us say you are growing lentils and they are not fairing well in your area but someone else says "Heck they perform great in my area!" I would be apt to say that the second person must have a greater population of Rhizobium leguminosarum in their soil.
If you are in question regarding planting beans and are wondering of their nitrogen fixation potential and you have never planted legumes in the area you are wishing to garden before, I would probably tell you to innoculate either the seeds or the soil itself when you plant. Make sure you have the right bacteria and your plant will form the relationship necessary to fix nitrogen. Once the bacteria is in the soil they can live there for years to come.
The excess nitrogen the legume took up through the relationship with the bacteria is released back into the soil and is made available for other plants when the legume has exceeded its need for that nitrogen.
It is a matter of how rampant the legume grows and how much the roots nodulate. There are two very effective nitrogen fixing crops that are commonly available. The are Hairy Vetch and Cowpeas, but with the cowpeas, you get best results with rampant climbing varieties.
There is also a climate effect with Alfalfa performing well in the arid west because of its deep root system, Cowpeas doing well in the humid south, and Vetch doing well in the midwest and parts of the east.
Ordinary beans (phaseolus vulgaris) are relatively ineffective at fixing nitrogen.
Mesquite trees :)
What's best for someone else's climate and soil may not be best for yours.
Alfalfa is supposed to be a great perennial, but it also prefers more alkaline soil than my 5.8. Others are more dependent on soil warmth, some dependent on regular moisture.
Maybe your local Cooperative Extension/Master Gardener could give you some leads. And the inoculant is important if the plant needs it.
Here is a link that might be useful: Coop. Ext. offices