I have been using sage to calculate conductors of elliptic curves defined over symbolic number fields (as the subject line indicates) and I came across a somewhat strange quirk. I initially was using the E.conductor() method, but as my curves got more complicated the RAM needed to do the calculations quickly grew beyond my computers capabilities. At school I have access to a computer with 16 gigs of RAM and even this was insufficient. As I read more and more on this issue I found the E.local_data() method that returns considerably more information about the given elliptic curve including local minimal models, exponent of conductors, valuations of minimal discriminants and Iwasawa numbers for all primes of bad reduction. I thought that because this method returns more information than is needed to calculate the conductor of an elliptic curve it would require even more RAM than the E.conductor() method. This was not the case by a long shot. I was able to do the calculations I needed on a computer that had less than a tenth of the RAM. My personal home computer only has 1.5 Gigs. I was curious if anyone knew why this is the case and if there was any attempt to recreate the conductor method using the local_dad method. Any input or insight would be much appreciated.
Thanks in advance, Harris Daniels
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