Let $\mathcal{E}$ be an elliptic surface over $\mathbb{P}^1$ without a section. What is a right definition of its Jacobian elliptic surface $J(\mathcal{E})$? Is it unique up to birational isomorphisms over $\mathbb{P}^1$? How can I find its Weierstrass equation $\mathcal{W}$?
2026-03-31 21:05:52.1774991152
Jacobian elliptic surface $J(\mathcal{E})$ for a given elliptic surface $\mathcal{E}$ without a section.
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