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When looking through elliptic curve and modulus posts i can see many examples of people referencing $p$ and $n$, in upper and lower case, and sometimes $Q$ is written instead of $p$ or $P$, and I think I've seen $N$ written as $Q$ once.

For example, this is one of the things I've seen for sepc256k1:

$p$ = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
$P$ = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
$n$ = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
$N$ = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
$Q$ = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f

I am confused about which is considered the correct way to write $p$, $n$ and $Q$. Is it considered better to use $Q$ instead of $p$? Is there an agreed standard? Does uppercase signify something different than lower case? I see a lot of things, and all of this wastes a lot of thinking energy worrying about the correctness of how to write a letter.

What is the correct way to notate elliptic curve properties?

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There is no standard way, and I think it's impossible to find universal agreement.

However, it is pretty common to use lowercase letters for integers and uppercase letters for elliptic curve points. And it is very common to indicate as p the prime defining the field $\mathbb F_p$ over which the curve is defined.

For the order of the curve you can use $\#E(\mathbb F_p)$, sometimes n is used but it is also common to use n to indicate the order of the largest prime order subgroup (note that if $\#E(\mathbb F_p)$ is prime then the two indicate the same value). Bernstein notably uses l to indicate the order of the largest prime order subgroup.

h is (I think) universally used to indicate the cofactor, such that $\#E(\mathbb F_p) = hl$

Also the curve's parameters are indicated as lowercase. For short Weierstrass curves you have a and b. For Twisted Edwards you have d and a.

For the points G, P, Q, B are quite common and if G is used then it indicates the generator of the largest prime order subgroup. Note that Bernstein uses B for the generator (Base).

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There is no standard (let alone correct) notation for elliptic curves, or anything else for that matter. It is up to each author to precisely state which notation is used for what.

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