Let $C$ be a smooth projective curve of genus $g$, let $c$ be a point in $C$. Let $(n\_1,\dots, n\_{g-1})$ be a $(g-1)$ tuple of nonzero integers. 


Consider the image $f\_{(n\_i)}\colon C^{g-1}\to \mathrm{Pic}^0(C)$ given by 
$$(x\_i)\mapsto \mathcal{O}\_C\left(\sum n\_i(x\_i-c)\right),$$
the image $\mathrm{Im}(f\_{(n\_i)})$ is a divisor in $\mathrm{Pic}^0(C)$. 


If $C$ is general, then $NS(C)$ is generated by theta divisor $\Theta$, so we can write numerical classes as a multiple of the theta divisor,
$$\mathrm{Im}(f\_{(n\_i)})=d(n\_1,\dots,n\_{g-1}）\Theta.$$


Is there a reference what are the functions $d$？


(In geometry of algebraic curves vol I, page 223, the case (1,..1,-1,..,-1) was considered, but there seems to be a typo)



Determining numerical class of divisors inside Jacobian
Let $C\_i$ be the image of $C$ by the multiplication map $JC \xrightarrow{\ \times n\_i\ }JC$. Your divisor is the image of the addition map $\mu : C\_1\times \ldots \times C\_{g-1}\rightarrow JC$. Its cohomology class is $(\deg \mu )^{-1}[C\_1]\*\ldots \* [C\_{g-1}]$, where "$\*$" is the Pontryagin product. Now the cohomology class $[C\_i]\in H^{2g-2}(JC,\mathbb{Z})$ is $n\_i^{2}[C]$, so 
$[C\_1]\*\ldots \* [C\_{g-1}]=$ $(\prod n\_i)^{2}[C]\*\ldots \* [C]=(\prod n\_i)^{2}(g-1)! [\Theta ]\ $ . 


Therefore $d(n\_1,\ldots ,n\_{g-1})=(\prod n\_i)^{2}\dfrac{(g-1)!}{\deg \mu }\,\cdot $ 


The remaining problem is to compute $\deg \mu $. I believe that if
$n\_1=\ldots =n\_a<n\_{a+1}=\ldots =n\_{a+b}< n\_{a+b+1}=\ldots $, we have $\deg \mu =a!b!\ldots $, but this should be checked.


