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Jun 6 at 16:23 comment added Navvye @ChrisWuthrich I agree. I'm interested in this because of a theorem by Silverman which gives an explicit upper bound for the number of integral solutions for these curves.
Jun 6 at 16:20 comment added Kevin Casto It seems like this comes down to showing that the proportion of rationals $A,B$ of a bounded height satisfying $4A^3 + 27B^2 \mid 1728\cdot 4A^3$ goes to 0.
Jun 6 at 16:04 history edited YCor CC BY-SA 4.0
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Jun 6 at 16:01 comment added Chris Wuthrich $j(E)\in\mathbb{Z}$ is a very strong assumption.
Jun 6 at 15:40 history asked Navvye CC BY-SA 4.0