  Let $E$ be an elliptic curve, with identity $O$, and let $C$ be a cyclic
subgroup of odd order $N$, over an algebraically closed field $k$ with
$\operatorname{char} k \nmid N$. For $P \in C$, let $s_P$ be a rational
function with divisor $N \cdot P - N \cdot O$. We ask whether the $N$ functions
$s_P$ are linearly independent. For generic $(E,C)$, we prove that the answer
is yes. We bound the number of exceptional $(E,C)$ when $N$ is a prime by using
the geometry of the universal generalized elliptic curve over $X_1(N)$. The
problem can be recast in terms of sections of an arbitrary degree $N$ line
bundle on $E$.
