I have an elliptic curve E defined over the rationals and K is an imaginary quadratic field. I have a Heegner point P for E over K. I also have a rational prime p. Let q be a prime of K above p. I would like to use Sage to check whether the point P is divisible by p in E(K) and also in E(Kq) where Kq is the completion of K at the prime q. To check this in E(K) is easy; one can use the heegner_index() function or one can use the division_points() function. I am wondering if there is a way in Sage to do my required check in E(Kq). It seems to me that completions of number fields at finite primes are not defined in Sage. One can define in sage Kq as an extension field of Qp but then one must consider P as an element of E(Kq) via an appropriate embedding and I'm unsure how to do this.
Any ideas on how I can do my local computation? I need to do a bunch of these local computations for a paper I'm working on. -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-nt/4ea171f6-a11b-4361-ac92-2f882b3223b0%40googlegroups.com.
