ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 02 Aug 2019 06:29:26 -0500characteristics three field elliptic curve lliptic curve for characteristics three fieldhttps://ask.sagemath.org/question/47347/characteristics-three-field-elliptic-curve-lliptic-curve-for-characteristics-three-field/How to generate elliptic curve from the following code as `B` is in hexadecimal form. The elliptic curve generated from the following code is ... which is not showing `B` in irreducible polynomial form.
**Elliptic Curve defined by $y^2 = x^3 + x^2 + 1$ over Finite Field in $a$ of size $3^{151}$**
F1.<x> = GF(3)[]
F.<a> = GF(3^151, 'a', modulus=x^151 + 2*x^2 + 1)
F.modulus()
F
A = 1
A
B = (0x1fc4865afe00a9216b0b5fd32c6300c4bed0707ae4072a03e55299f157b)
B
E = EllipticCurve(F, (0, A, 0, 0, B))
EFri, 02 Aug 2019 05:51:15 -0500https://ask.sagemath.org/question/47347/characteristics-three-field-elliptic-curve-lliptic-curve-for-characteristics-three-field/Answer by rburing for <p>How to generate elliptic curve from the following code as <code>B</code> is in hexadecimal form. The elliptic curve generated from the following code is ... which is not showing <code>B</code> in irreducible polynomial form.</p>
<p><strong>Elliptic Curve defined by $y^2 = x^3 + x^2 + 1$ over Finite Field in $a$ of size $3^{151}$</strong></p>
<pre><code>F1.<x> = GF(3)[]
F.<a> = GF(3^151, 'a', modulus=x^151 + 2*x^2 + 1)
F.modulus()
F
A = 1
A
B = (0x1fc4865afe00a9216b0b5fd32c6300c4bed0707ae4072a03e55299f157b)
B
E = EllipticCurve(F, (0, A, 0, 0, B))
E
</code></pre>
https://ask.sagemath.org/question/47347/characteristics-three-field-elliptic-curve-lliptic-curve-for-characteristics-three-field/?answer=47349#post-id-47349The field $F = GF(3^{151})$ is a 151-dimensional vector space over $GF(3)$, so its elements can be viewed as vectors of length 151 with entries in $\{0,1,2\}$, or as natural numbers $< 3^{151}$ written in base 3. To do the conversion in SageMath, you can do:
B = F(B.digits(3))Fri, 02 Aug 2019 06:29:26 -0500https://ask.sagemath.org/question/47347/characteristics-three-field-elliptic-curve-lliptic-curve-for-characteristics-three-field/?answer=47349#post-id-47349