diff --git a/lmfdb/ecnf/WebEllipticCurve.py b/lmfdb/ecnf/WebEllipticCurve.py
index bd8651fcc0..22b64cb83b 100644
--- a/lmfdb/ecnf/WebEllipticCurve.py
+++ b/lmfdb/ecnf/WebEllipticCurve.py
@@ -2,7 +2,7 @@
 from flask import url_for
 from urllib.parse import quote
 from markupsafe import Markup, escape
-from sage.all import (Infinity, PolynomialRing, QQ, RDF, ZZ, KodairaSymbol,
+from sage.all import (Infinity, PolynomialRing, QQ, RDF, ZZ, RR, KodairaSymbol,
                       implicit_plot, plot, prod, rainbow, sqrt, text, var)
 from lmfdb import db
 from lmfdb.utils import (encode_plot, names_and_urls, web_latex, display_knowl,
@@ -494,7 +494,8 @@ def make_E(self):
             self.mw_struct = "unknown"
 
         # Torsion
-        self.ntors = web_latex(self.torsion_order)
+        BSDntors = self.torsion_order
+        self.ntors = web_latex(BSDntors)
         self.tr = len(self.torsion_structure)
         if self.tr == 0:
             self.tor_struct_pretty = "$0$"
@@ -563,18 +564,28 @@ def make_E(self):
                 self.bsd_status = "missing_gens"
 
         # Regulator only in conditional/unconditional cases, or when we know the rank:
+        BSDReg = None
         if self.bsd_status in ["conditional", "unconditional"]:
             if self.ar == 0:
-                self.reg = web_latex(1)  # otherwise we only get 1.00000...
+                BSDReg = 1
+                self.reg = self.NTreg = web_latex(BSDReg)  # otherwise we only get 1.00000...
             else:
                 try:
-                    self.reg = web_latex(self.reg)
+                    R = self.reg
+                    BSDReg = R * K.degree()**self.rank
+                    self.reg = web_latex(R)
+                    self.NTreg = web_latex(BSDReg)
                 except AttributeError:
                     self.reg = "not available"
+                    self.NTreg = "not available"
         elif self.rk != "not available":
-            self.reg = web_latex(self.reg) if self.rank else web_latex(1)
+            R = self.reg
+            BSDReg = R * K.degree()**self.rank
+            self.reg = web_latex(R) if self.rank else web_latex(1)
+            self.NTreg = web_latex(BSDReg) if self.rank else web_latex(1)
         else:
             self.reg = "not available"
+            self.NTreg = "not available"
 
         # Generators
         try:
@@ -585,17 +596,31 @@ def make_E(self):
             self.gens = []
             self.gens_and_heights = []
 
-        # Global period
+        # Global period -- see issue #5409 for why we multiply by
+        # 2**nc in most cases.  However, data computed after
+        # 2024-07-09 (including all data for imaginary quadratic
+        # fields of absolute discriminant > 600 as well as some larger
+        # conductors for other IQFs) already has the extra factor of
+        # 2.  As a fail-safe until we fix the data in all cases, we
+        # will test (using the BSD formula) whether to remove the
+        # factor of 2 added here.
+        BSDomega = None
         try:
-            self.omega = web_latex(self.omega)
+            BSDomega = self.omega
+            nc = self.signature[1] # number of complex places
+            if nc:
+                BSDomega *= 2**nc
+            self.omega = web_latex(BSDomega)
         except AttributeError:
             self.omega = "not available"
 
         # L-value
+        BSDLvalue = None
         try:
             r = int(self.analytic_rank)
             # lhs = "L(E,1) = " if r==0 else "L'(E,1) = " if r==1 else "L^{{({})}}(E,1)/{}! = ".format(r,r)
-            self.Lvalue = web_latex(self.Lvalue)
+            BSDLvalue = self.Lvalue
+            self.Lvalue = web_latex(BSDLvalue)
         except (TypeError, AttributeError):
             self.Lvalue = "not available"
 
@@ -607,14 +632,79 @@ def make_E(self):
             self.tamagawa_factors = r'\cdot'.join(cp_fac)
         else:
             self.tamagawa_factors = None
-        self.tamagawa_product = web_latex(prod(tamagawa_numbers,1))
+        BSDprodcp = prod(tamagawa_numbers,1)
+        self.tamagawa_product = web_latex(BSDprodcp)
 
         # Analytic Sha
+        BSDsha = None
         try:
-            self.sha = web_latex(self.sha) + " (rounded)"
+            BSDsha = self.sha
+            self.sha = web_latex(BSDsha) + " (rounded)"
         except AttributeError:
             self.sha = "not available"
 
+        # Check analytic Sha value compatible with formula in the knowl (see issue #5409)
+
+        BSDrootdisc = RR(K.discriminant().abs()).sqrt()
+        BSDok = True
+        if BSDLvalue and BSDsha and BSDReg and (self.rank is not None):
+            BSDsha_numerator = BSDrootdisc * BSDntors**2
+            BSDsha_denominator = BSDReg * BSDomega * BSDprodcp
+            BSDsha_from_formula = BSDLvalue * BSDsha_numerator / BSDsha_denominator
+            BSDsha_from_formula_rounded = BSDsha_from_formula.round()
+            BSDok = (BSDsha_from_formula_rounded == BSDsha) and ((BSDsha_from_formula_rounded -BSDsha_from_formula).abs() < 0.001)
+            #print(f"{BSDsha_from_formula=}")
+            #print(f"{BSDsha_from_formula_rounded=}")
+            #print(f"{BSDsha=}")
+            #print(f"{BSDok=}")
+            if not BSDok:
+                # this means that we doubled BSDomega when we should
+                # not have, so BSDsha_denominator is doubled and
+                # BSDsha_from formula is halved
+                print(f"BSD normalization: adjusting Omega for {self.label}: stored Sha = {BSDsha} but formula gives {BSDsha_from_formula}")
+                BSDok = ((BSDsha/BSDsha_from_formula)-2).abs() < 0.01
+                if not BSDok:
+                    print(f"BSD normalization issue with {self.label}: stored Sha = {BSDsha} but formula gives {BSDsha_from_formula}")
+                BSDomega /= 2
+                BSDsha_denominator /= 2
+                BSDsha_from_formula *= 2
+                BSDsha_from_formula_rounded = BSDsha_from_formula.round()
+            BSDLvalue_from_formula = BSDsha * BSDsha_denominator / BSDsha_numerator
+            self.BSDsha = web_latex(BSDsha_from_formula)
+            self.BSDLvalue = web_latex(BSDLvalue_from_formula)
+
+            # The BSD formula for display
+
+            dot = '\\cdot'
+            approx = '\\approx'
+            eq_query = '\\overset{?}{=}'
+            frac = '\\frac'
+            Sha = '\\# &#1064;(E/K)'
+            Om = '\\Omega(E/K)'
+            Reg = '\\mathrm{Reg}_{\\mathrm{NT}}(E/K)'
+            prodcp = '\\prod_{\\mathfrak{p}} c_{\\mathfrak{p}}'
+            tors2 = '\\#E(K)_{\\mathrm{tor}}^2'
+            rootD = '\\left|d_K\\right|^{1/2}'
+
+            lder_name  = rf"L^{{({r})}}(E/K,1)/{r}!" if r>=2 else "L'(E/K,1)" if r else "L(E/K,1)"
+            lhs_num    = rf'{Sha} {dot} {Om} {dot} {Reg} {dot} {prodcp}'
+            lhs_den    = rf'{tors2} {dot} {rootD}'
+            lhs        = rf'{frac}{{ {lhs_num} }} {{ {lhs_den} }}'
+            rhs_num    = rf'{BSDsha} {dot} {BSDomega:0.6f} {dot} {BSDReg} {dot} {BSDprodcp}'
+            if r:
+                rhs_num    = rf'{BSDsha} {dot} {BSDomega:0.6f} {dot} {BSDReg:0.6f} {dot} {BSDprodcp}'
+            rhs_den    = rf'{{{BSDntors}^2 {dot} {BSDrootdisc:0.6f}}}'
+            rhs        = rf'{frac}{{ {rhs_num} }} {{ {rhs_den} }}'
+            self.bsd_formula = rf'{BSDLvalue:0.9f} {approx} {lder_name} {eq_query} {lhs} {approx} {rhs} {approx} {BSDLvalue_from_formula:0.9f}'
+
+        else:
+            self.BSDsha = "not available"
+            self.BSDLvalue = "not available"
+            self.bsd_formula = None
+
+        if not BSDok: # don't display the formula if it is not correct
+            self.bsd_formula = None
+
         # Local data
 
         # The Kodaira symbol is stored as an int in pari encoding. The
diff --git a/lmfdb/ecnf/templates/ecnf-curve.html b/lmfdb/ecnf/templates/ecnf-curve.html
index d5a48fa4d7..e288520570 100644
--- a/lmfdb/ecnf/templates/ecnf-curve.html
+++ b/lmfdb/ecnf/templates/ecnf-curve.html
@@ -274,7 +274,7 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 	<tr>
 	  <td align='left'>{{ KNOWL('ec.rank', title="Mordell-Weil rank")}}:</td>
 	  {% if ec.rk == "not available" %}
-	  <td>$r$?</td>
+	  <td>$r?$</td>
 	  <td>&nbsp;</td>
 	  {% if ec.rank_bounds != "not available" %}
 	  <td>\({{ ec.rk_lb }} \le r \le {{ec.rk_ub}}\)</td>
@@ -296,7 +296,7 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 	    {% endif %}
 	  </td>
 	  <td>$\mathrm{Reg}(E/K)$</td>
-	  <td>{% if ec.rk == 0 %}={% else %}&approx;{% endif %}</td>
+	  <td>{% if ec.rank == 0 %}={% else %}&approx;{% endif %}</td>
           <td>
 	  {% if ec.reg=='not available' %}
 	  not available
@@ -305,6 +305,24 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 	  {% endif %}
 	</td>
         </tr>
+        <tr>
+	  <td align='left'>
+	    {% if ec.bsd_status == "conditional" %}
+            {{ KNOWL('ec.regulator', title='N&eacute;ron-Tate Regulator*') }}:
+	    {% else %}
+	    {{ KNOWL('ec.regulator', title='N&eacute;ron-Tate Regulator') }}:
+	    {% endif %}
+	  </td>
+	  <td>$\mathrm{Reg}_{\mathrm{NT}}(E/K)$</td>
+	  <td>{% if ec.rank == 0 %}={% else %}&approx;{% endif %}</td>
+          <td>
+	  {% if ec.NTreg=='not available' %}
+	  not available
+	  {% else %}
+	  {{ ec.NTreg }}
+	  {% endif %}
+	</td>
+        </tr>
 
         <tr>
         <td align='left'>{{ KNOWL('ec.period', title='Global period') }}:</td>
@@ -349,8 +367,19 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 	  <td>&#1064;${}_{\mathrm{an}}$</td><td>=</td>
           <td> {{ ec.sha }} </td>
         </tr>
+{#
+	<tr>
+	  <td align='left'>
+	    {{ KNOWL('ec.analytic_sha_order', title='Analytic order of &#1064; (from formula)') }}:
+	  </td>
+	  <td>&#1064;${}_{\mathrm{an}}$</td><td>=</td>
+          <td> {{ ec.BSDsha }} </td>
+        </tr>
+#}
         </table>
-    </p>
+{# %%%%%%%%%%%%%%%% END OF TABLE %%%%%%%%%%%%%%%%%%% #}
+</p>
+
 {% if ec.bsd_status == "conditional" %}
 <p>
   * Conditional on {{ KNOWL('ec.bsdconjecture', title='BSD') }}: assuming rank = analytic rank.
@@ -364,10 +393,22 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 </p>
 {% endif %}
 {% endif %}
+</div>
 
-{# %%%%%%%%%%%%%%%% END OF TABLE %%%%%%%%%%%%%%%%%%% #}
+{% if ec.bsd_formula %}
+
+<h2> {{ KNOWL('ec.bsdconjecture', title='BSD formula') }}</h2>
+<div>
+<p style="margin:10px 280px;">
+$\displaystyle {{ ec.bsd_formula|safe }}$
+</p>
+<center>
+{{ place_code('bsd_formula') }}
+</center>
 </div>
 
+{% endif %}
+
 <h2>{{KNOWL('ec.local_data', title='Local data')}} at {{KNOWL('ec.bad_reduction', title='primes of bad reduction')}} </h2>
 <div>
  {{ place_code('localdata') }}