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Elliptic curves downloaded from the LMFDB downloaded on 23 September 2023.
Below is a list called data. Each entry has the form:
[[field_poly],[Weierstrass Coefficients, constant first in increasing degree]]
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R,x = PolynomialRing(QQ);
data = [
[[x^2 + 2], [[1,0],[1,-1],[0,1],[-5,-4],[-1,3]]],
[[x^2 + 2], [[1,1],[0,0],[1,0],[-7,2],[-6,2]]],
[[x^2 + 2], [[1,1],[0,0],[0,1],[-68,55],[72,-228]]],
[[x^2 + 2], [[1,0],[1,-1],[1,0],[55,78],[569,73]]]]