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

   - CITE{LMFDB}   rigour: assumed-bound-  rigour details: The computed interval was widened by four units in the last place-    (blur_real_interval). That bound was asserted rather than derived, and the justification-    was not recorded.+  rigour details: 'Computed with Sage''s E.regulator(proof=True). The arithmetic is+    proven: proof=True means the Mordell-Weil basis is certified, so the regulator+    is the right quantity rather than a multiple of it. The numerics are not. The+    heights come from PARI''s ellheight, whose documentation states the normalisation+    and nothing about accuracy; Sage''s own implementation truncates Silverman''s+    series at a term count derived from his published bound, but tracks no rounding+    error through the loop, and its working precision is a guard found by patching+    cases that failed. The height pairing matrix is then built in ordinary floating+    point, its off-diagonal entries by a subtraction of nearly equal heights, and+    a determinant is taken. Recomputing at double precision agrees to about 204 digits,+    so the hundred written here are almost certainly right; nothing bounds them.' Display properties:   number-header: $\text{Reg}(E/\mathbb{Q})$