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The statement of the theorem seems wrong. According to OEIS the number 11 is not a congruent number, yet the criterion as stated on the page implies that it is congruent (assuming BSD). Indeed note that
A_11 = 4 since we have the solutions (1, 3, 0), (-1, 3, 0), (1, -3, 0), (-1, -3, 0) and B_11 = 8 since we have the 8 solutions corresponding to all sign combinations of (1, 1, 1).
Can someone care to explain what is going on? Or perhaps correct the statement? As stated on wiki this statement does not appear in Tunnell's paper (he expresses the conditions in terms of the coefficients of the half-integral forms) so perhaps an error slipped in during the simplification of the statement. — Preceding unsigned comment added by 166.164.37.191 (talk) 21:46, 2 August 2015 (UTC)
- The solutions you found for A are also solutions for B (look what happens when z = 0.) Dong, where is my automobile? (talk) 03:01, 3 August 2015 (UTC)