<p>From what I can find about this concept, rank of an elliptic curve is only defined for elliptic curves over the rational numbers.</p>
<p>Since secp256k1 is an elliptic curve defined over a finite field, the term does not apply.</p>
<p>The elliptic curve <em>y<sup>2</sup> = x<sup>3</sup> + 7</em>, over the rational numbers, has rank 0.</p>

CC BY-SA 4.0
2024-11-16T21:50:31.133Z
I was indeed talking about prime fields. While of course, it doesn’t apply to Bitcoin I was reading [this paper](https://ieeexplore.ieee.org/abstract/document/6767331/) that propose a practical algorithm for solving discrete logarithms if the underlying curve has rank 1. **So I was curious to know what was the rank of secp256k1**.
user2284570
CC BY-SA 4.0
2024-11-16T22:14:07.040Z
I can't access that paper, but are you sure it's about solving ECDLP over a finite field?
Pieter Wuille
CC BY-SA 4.0
2024-11-17T05:31:32.903Z
Yes I am. The full pdf is here https://pdfupload.io/docs/4ef85049
user2284570
CC BY-SA 4.0
2024-11-16T21:01:57.200Z
2024-11-16T21:01:57.200Z
Pieter Wuille
<p>Simple question. I failed to find how compute the rank of an elliptic curve using the version of online tools like SageMath or Pari/gp since it’s the only thing I have access to…</p>
<p>So elliptic curves have a something that is called <strong>a rank</strong>. What’s the rank of secp256k1 or how to compute it using SageMath or Pari/gp ?</p>

<security><secp256k1><math><elliptic-curve>
What’s the curve rank of secp256k1?
user2284570
# What’s the curve rank of secp256k1?

(Asked by: username_0 on 2024-11-16)

Simple question. I failed to find how compute the rank of an elliptic curve using the version of online tools like SageMath or Pari/gp since it’s the only thing I have access to…

So elliptic curves have a something that is called **a rank**. What’s the rank of secp256k1 or how to compute it using SageMath or Pari/gp ?

**Tags:** security, secp256k1, math, elliptic-curve


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## 1 answers

### Answer by username_1 on 2024-11-16. Score: 2

From what I can find about this concept, rank of an elliptic curve is only defined for elliptic curves over the rational numbers.

Since secp256k1 is an elliptic curve defined over a finite field, the term does not apply.

The elliptic curve *y2 = x3 + 7*, over the rational numbers, has rank 0.

> **Comments:**
> **username_0**: I was indeed talking about prime fields. While of course, it doesn’t apply to Bitcoin I was reading [this paper](https://ieeexplore.ieee.org/abstract/document/6767331/) that propose a practical algorithm for solving discrete logarithms if the underlying curve has rank 1. **So I was curious to know what was the rank of secp256k1**.  
> **username_1**: I can't access that paper, but are you sure it's about solving ECDLP over a finite field?  
> **username_0**: Yes I am. The full pdf is here https://pdfupload.io/docs/4ef85049  

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