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Is there some clever way to integrate products of elliptic functions $\wp(z;g_2,g_3)$ or $\zeta(z;g_2,g_3)$ in Mathematica?

Mathematica seems to be able to integrate functions like

Integrate[WeierstrassP[z, {g2, g3}]^3, z]

However, not something like

Integrate[WeierstrassP[z, {g2, g3}] WeierstrassP[z + a, {g2, g3}]], z]

I have tried using the addition formulae for the $\wp(z)$, but Mathematica is still unable to give the answer.

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