Relation between logistic regression coefficient and odds ratio in JMP

From the output of a logistic regression in JMP, I read about two binary variables:

Var1 estimate -0.1007384
Var2 estimate  0.21528927


and then

Odds ratio for Var1 lev1/lev2 1.2232078 reciprocal 0.8175225
Odds ratio for Var2 lev1/lev2 0.6501329 reciprocal 1.5381471


Now I obtain 1.2232078 as exp(2*0.1007384), and similarly for the other odds ratio.

So, my question is: why I have to multiply by two? Is the relation between a coefficient c and its odds ratio r equal to r=exp(c)? Isn't it?

Ok, I drop a quick response. Your idea is correct in that the regression coefficient is the log of the OR. More precisely, if $b$ is your regression coefficient, $\exp(b)$ is the odds ratio corresponding to a one unit change in your variable. So, to get back to the adjusted odds, you need to know what are the internal coding convention for your factor levels. Usually, for a binary variable it is 0/1 or 1/2. But if it happens that your levels are represented as -1/+1 (which I suspect here), then you have to multiply the regression coefficient by 2 when exponentiating.
The same would apply if you were working with a continuous variable, like age, and want to express the odds for 5 years ($\exp(5b)$) instead of 1 year ($\exp(b)$).