We give some numerical data on the quadratic twists by negative discriminants of the first smallest (for the conductor) elliptic curves. For each curve (11a1, 14a1, 15a1 and 17a1), the file contains a PARI/GP vector W of length 1500000 such that W[b] is non-zero iff -b is a fundamental discriminant and satisfying additional conditions so that the sign of the functional equation is -1. In that case, W[b] then contains a vector whose entries are: 1) the short ellinit of the minimal Weierstrass model of the quadratic twist, 2) the product of the Tamagawa numbers, 3) a generator of the Mordell-Weil group, 4) the analytic order of the Tate-Shafarevich group, 5) the index of the subgroup generated by torsion and the Heegner point used in the computation. Note that if the analytic rank of the quadratic twist is greater than 1 then the last three entries are zero.
[Data]
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