Nontorsion points of low height on elliptic curves over Q

The following table lists the 54 cases known to me of pairs (E,P) where E is an elliptic curve over Q and P is a nontorsion point on E of canonical height h<1/100. The curves are listed in order of increasing h. For each curve we list the conductor N, the coordinates (A,u) of (E,P) [explicit formulas below] the coefficients (a₁, a₂, a₃) (where E is Y² + a₁ XY + a₃ Y = X³ + a₂ X² and P is (0,0)), and the positive integers n<=50 such that nP is an integral point on the minimal model of E, followed by the count of such n. These were found by an exhaustive search over (A,u); William Stein confirms that the list includes all 32 instances of N<12000, using the extended Cremona tables. This list also contains the highest known integral multiple (n=31, at #10), the largest counts of integral multiples (16, at #1 and #2), and the largest known ratio log|D|/h (11822.2+, at #44; the next largest is 9388.9+ at #1).
As for the most consecutive integral multiples, the table lists several instances of 12, and in fact I can prove that there are infinitely many cases where nP is integral for each n=1,2,...,12; but that is not the record: there are several 13's, and one 14. The choice (A,u)=(-45/41,-12/5) yields a curve E of conductor 1029210 with coefficients (a₁, a₂, a₃) = (209,23520,2446080) and a point P=(0,0) whose height of 0.01017273 places it just beyond our table's range but whose first 14 multiples (and also the 18th) are integral points on E.

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