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Good Day. I'm sorry for my sage code, without formulas, but I looking your help friend.

p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
F = FiniteField(p)
E = EllipticCurve(F,[0,7])
print(E[0])

what mean E[0] ????

It very hard to calculate E[0], so, I'm looking for your help friends.

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  • $\begingroup$ Could you ask at ask.sagemath.org ? $\endgroup$
    – kelalaka
    Jan 31 at 22:26
  • $\begingroup$ This is cryptography quescion kalalalaka. Thank you for your answer. Can you help ? $\endgroup$
    – Donald
    Jan 31 at 22:29
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    $\begingroup$ As you see this has nothing to do with cryptography.se. It is all about how the SageMath is working. $\endgroup$
    – kelalaka
    Feb 1 at 14:19
  • $\begingroup$ Are you after the order $n$ of the group for secp256k1? Yes it's an involved computation, but that's not a secret. PS: It tried to migrate the question to SO, but the system didn't agree, and closed it. $\endgroup$
    – fgrieu
    Feb 1 at 15:31
  • $\begingroup$ And don't cross-post; math $\endgroup$
    – kelalaka
    Feb 1 at 18:52
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E[n] returns the $n$-th point in its list of $F$-rational points.

Source: __getitem__ in

https://github.com/sagemath/sage/blob/develop/src/sage/schemes/elliptic_curves/ell_finite_field.py

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  • $\begingroup$ Ok. And why E[0] eating 256 GB computer memory and noting found ? What answer of E[0] ??? $\endgroup$
    – Donald
    Jan 31 at 23:16
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    $\begingroup$ Because your curve is too large and it tries to generate the list of $F$-rational points before returning you the first element. $\endgroup$
    – Myath
    Jan 31 at 23:17
  • $\begingroup$ Okey. And there is a dictionary about this rational point ? $\endgroup$
    – Donald
    Jan 31 at 23:18
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    $\begingroup$ $F$-rational points are just points with coordinates in $F$. $\endgroup$
    – Myath
    Jan 31 at 23:19
  • $\begingroup$ Myath, this is not simple coordinates - this like: sage: E = EllipticCurve('11a'); E Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field sage: P = E(0); P (0 : 1 : 0) $\endgroup$
    – Donald
    Jan 31 at 23:43

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