History of Real periods of elliptic curves over $\mathbb{Q}$ of rank $3$

   sources:   - CITE{LMFDB} (list of curves with bounded conductor)-  rigour: heuristic (agreement-checked)-  rigour details: 'Computed at two working precisions and written only after the two-    agreed. The underlying computation is pi divided by an arithmetic-geometric mean-    in ordinary floating point: quadratically convergent and about as well behaved-    as a transcendental computation gets, but with no error bound carried through-    it. This one could be proven -- arb implements the AGM in ball arithmetic, and-    at 700 bits gives the real period to 695 accurate bits from exact algebraic input-    -- and should be, when a generator replaces the script.'+  rigour: proven+  rigour details: Recomputed in ball arithmetic and verified entry by entry. Sage+    computes the real period as pi divided by an arithmetic-geometric mean in ordinary+    floating point, with no error bound carried through it; arb has the agm in ball+    arithmetic, so the same identity applied to the curve's exact algebraic invariants+    gives an enclosure instead. Every entry of this table agrees with one, at around+    395 accurate bits out of 400. The curve is taken from the entry's own c-invariants,+    which determine it, and its conductor checked against the entry's N. Display properties:   number-header: $\omega_1$