So I was trying to compute a normalized model of elliptic curve as described here. Consider $p$= 5326738796327623094747867617954605554069371494832722337612446642054009560026576537626892113026381253624626941643949444792662881241621373288942880288065659, and $\mathbb{F}_p$-rational roots of $\Phi_{37}(1728,Y)$ being $1728, 1720807343354842318, 486633164864362301,$ each with multiplicity 2. Take any one as $j_{37}$, then it turns out $\Phi_Y(1728,j_{37})$ all leads to zero. This would cause the normalization procedure to crash because of division-by-zero.

Did I do something wrong? How should I deal with this problem? And perhaps more importantly, what does these zeros intuitively indicate?


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