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Co-authored-by: Vincent Macri <[email protected]>

src/sage/schemes/elliptic_curves/ell_finite_field.py

@@ -2873,7 +2873,7 @@ def EllipticCurve_with_prime_order(N):
     - ``N`` -- integer; the order for which we seek an elliptic curve. Must be a
       prime number.
 
-    OUTPUT: an iterator of elliptic curves `E/\mathbb F_p` of order ``N``
+    OUTPUT: an iterator of (some) elliptic curves `E/\mathbb F_p` of order ``N``
 
     .. NOTE::
 
@@ -2883,11 +2883,11 @@ def EllipticCurve_with_prime_order(N):
         of rounds that is polynomial in `\log\log N`. In practice (cf. Section
         5), this number is usually 1.
 
-    ALGORITHM: [BS2007]_, Algorithm 2.2
+    ALGORITHM: Based on [BS2007]_, Algorithm 2.2
 
     EXAMPLES::
 
-        sage: N = next_prime(int.from_bytes(b'sagemath', 'big'))
+        sage: N = 8314040072427107567
         sage: E = next(EllipticCurve_with_prime_order(N))
         sage: E
         Elliptic Curve defined by y^2 = x^3 + 4757897140353078952*x + 1841350074072114366
@@ -2913,7 +2913,7 @@ def EllipticCurve_with_prime_order(N):
 
     It works for large primes::
 
-        sage: N = 0x6cbc824032974516623e732462f4b74b56c4ffbd984380d9
+        sage: N = 2666207849820848272386538889527600954292544013630953455833
         sage: E = next(EllipticCurve_with_prime_order(N)); E
         Elliptic Curve defined by y^2 = x^3 + 2666207849820848272386538889427721639173508298483739490459*x
          + 77986137112576 over Finite Field of size 2666207849820848272386538889427721639173508298487130585243