# Calculating elliptic curve isogeny from a kernel polynomial

This question is related to my previous question, where I got partial answer to my problem. I have a code segment in Sage that roughly looks like this:

```
p = 10354717741769305252977768237866805321427389645549071170116189679054678940682478846502882896561066713624553211618840202385203911976522554393044160468771151816976706840078913334358399730952774926980235086850991501872665651576831
# Prime field of order p
Fp = GF(p)
R.<x> = PolynomialRing(Fp)
# The quadratic extension via x^2 + 1 since p = 3 mod 4
Fp2.<j> = Fp.extension(x^2 + 1)
E = EllipticCurve(Fp2, [1,0])
for e in range(200, 0, -2):
# Some calculation here, which produces a polynomial,
# let's call the polynomial generated is called "ker"
phi = EllipticCurveIsogeny(E, ker)
```

The point is that this throws an error also shown in my other question, which is `NotImplementedError: For basic Kohel's algorithm, if the kernel degree is even then the kernel must be contained in the two torsion.`

. In the other question I got one answer as to compute an actual point that generates the isogeny and use it in the `EllipticCurveIsogeny`

function. Though, is there a way in Sage to compute a point that generates the isogeny, from the kernel polynomial that generates the isogeny? Also if someone is interested here is a list of some kernel polynomials that I have generated. I have multiple loops that look like in the above example, so I need one universal solution so that I can apply to all my loops. Any ideas how to achieve what I want?

The pastebin is gone...

This page is no longer available. It has either expired, been removed by its creator, or removed by one of the Pastebin staff.Is it possible to compute the zeros of the

`ker`

? Do the corresponding "$x$-values" lift to some points of "small torsion" on`E`

?I updated the question with the new Pastebin. It appears the link had expired.