From 0dcbc7e11409d13df4d2c3d452ef9031dfcee235 Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Sat, 20 Dec 2025 00:51:57 +0700
Subject: [PATCH] Implement analytic_rank() for EllipticCurve_number_field

---
 .../schemes/elliptic_curves/ell_number_field.py   | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py
index 37af9dcba1f..c4489f62f52 100644
--- a/src/sage/schemes/elliptic_curves/ell_number_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py
@@ -2281,6 +2281,21 @@ def rank(self, **kwds):
         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.