amatar's profile - activity

I have an elliptic curve E defined over the rationals and K is a quadratic imaginary field. I have a Heegner point P for E over K. I also have a 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 that P is divisible by p in E(K) is easy; we can use the heegner_index() function or division_points() function. However I'm unsure how to do my required check in E(Kq). It seems to me that completions of number fields at finite primes are not supported in Sage. Any ideas whether I can use Sage to do this required check?

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.

Consider the elliptic curve E=EllipticCurve('37a')

This elliptic curve has rank 1 over $\mathbb{Q}$. I am interested in knowing which primes divide the index of the Heegner point $y_K$ in the group $E(K)$ modulo torsion where $K=\mathbb{Q}(\sqrt{-7})$

Since $E$ has rank 1, heegner_index_bound() does not work so I try E.heegner_index(-7). The output is 1.00000?

This output should be an interval. I do not understand the output. What does the question mark mean?