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Sep 28, 2014 at 22:07 comment added Mike Bennett In practice, one uses techniques based upon linear forms in elliptic logarithms because that's what the people who wrote the code in Magma and Sage used. For curves of even moderately high rank (whatever that means) one would expect that going via complex logarithms would be much faster.
Sep 28, 2014 at 21:28 history edited James Weigandt CC BY-SA 3.0
clarified some points
Sep 28, 2014 at 21:15 history edited James Weigandt CC BY-SA 3.0
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Sep 28, 2014 at 21:07 history answered James Weigandt CC BY-SA 3.0