Let $E$ be the elliptic curve $$y^2 =x^3 - 19*67 x$$ and $P=[26011/625,2159616/15625]$, I want to compute $\hat{h}(P)$ using formula given in

Fujita, Y., & Terai, N. (2011). Generators for the elliptic curve $ y^ 2= x^ 3-nx$. Journal de théorie des nombres de Bordeaux, 23(2), 403-416.

To compute Archimedean part (formula (3.2) in the article), we should to compute $\log{\theta}$, there is a formula in the article: $$\theta=\sum_{k=0}^{\infty}{(-1)^kq^{k(k+1)/2}sin((2k+1)\frac{2\pi}{\omega_1}Re(z))}$$ Is there a command in Pari/GP or Magma to compute this value? As mentioned in the article, $|\theta|<1/(1-q)$, is there a lower bound for $|\theta|$ in elliptic curves of the form $y^2=x^3-nx$?