Implement analytic_rank() for EllipticCurve_number_field

src/sage/schemes/elliptic_curves/ell_number_field.py

@@ -797,7 +797,7 @@
             sage: K.<a> = QuadraticField(4569)
             sage: j = 46969655/32768
             sage: E = EllipticCurve(j=K(j))
             sage: C = E.isogeny_class()                                                 # long time (9.5s)
         """
         K = self.base_field()
         r1, r2 = K.signature()
@@ -2281,6 +2281,21 @@
         else:
             raise ValueError('There is insufficient data to determine the rank - 2-descent gave lower bound %s and upper bound %s' % (lower, upper))
 
+    def analytic_rank(self):
+        r"""
+        Return an integer that is *probably* the analytic rank of this
+        elliptic curve.
+
+        EXAMPLES::
+
+            sage: K.<s> = QuadraticField(229)
+            sage: EllipticCurve("389a1").change_ring(K).analytic_rank()  # long time
+            3
+            sage: len(EllipticCurve("389a1").change_ring(K).gens())  # long time
+            3
+        """
+        return ZZ(self.integral_model().pari_curve().lfuncreate().lfunorderzero())
+
     def gens(self, **kwds):
         r"""
         Return some points of infinite order on this elliptic curve.