I'm trying to build intuition on how to construct elliptic curves satisfying some predetermined properties. I'm working on these two cases atm:(adsbygoogle = window.adsbygoogle || []).push({});

1) I can construct an elliptic curve with a point of order n, but how should I proceed if I want to ensure that the curve has also rank > 0? (I.e. I want also a point of inf order). Is there a standard method to do so?

2) In computing the order of the tors group, I'm interested in those curves for which knowing that #E(Q)|#E(F_p) is not sufficient to determine #E(Q). Does anyone have an example of such a curve? In general, how can one construct elliptic curves with this property?

Any help with either 1 or 2 is much appreciated

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Constructing elliptic curves

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**