diff --git a/lmfdb/ecnf/WebEllipticCurve.py b/lmfdb/ecnf/WebEllipticCurve.py
index e664325bcb..5992ac678c 100644
--- a/lmfdb/ecnf/WebEllipticCurve.py
+++ b/lmfdb/ecnf/WebEllipticCurve.py
@@ -487,7 +487,7 @@ def make_E(self):
         self.ntors = web_latex(self.torsion_order)
         self.tr = len(self.torsion_structure)
         if self.tr == 0:
-            self.tor_struct_pretty = "trivial"
+            self.tor_struct_pretty = "$0$"
         if self.tr == 1:
             self.tor_struct_pretty = r"\(\Z/%s\Z\)" % self.torsion_structure[0]
         if self.tr == 2:
diff --git a/lmfdb/ecnf/templates/ecnf-curve.html b/lmfdb/ecnf/templates/ecnf-curve.html
index e7682d3ec5..4d030ff796 100644
--- a/lmfdb/ecnf/templates/ecnf-curve.html
+++ b/lmfdb/ecnf/templates/ecnf-curve.html
@@ -76,6 +76,8 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>
       <table id="invariants" style="overflow:auto;">
         <tr>
         <td>{{KNOWL('ec.conductor', title='Conductor')}}:</td>
+	<td>$\frak{n}$</td>
+	<td>=</td>
         <td>{{ ec.cond }}</td>
         <td>=</td>
         <td>{{ ec.fact_cond }}</td>
@@ -84,6 +86,8 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>
 
         <tr>
         <td>{{KNOWL('ec.conductor', title='Conductor norm')}}:</td>
+	<td>$N(\frak{n})$</td>
+	<td>=</td>
         <td>{{ ec.cond_norm }}</td>
         <td>=</td>
         <td>{{ ec.fact_cond_norm }}</td>
@@ -92,6 +96,8 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>
 
         <tr>
         <td>{{KNOWL('ec.discriminant', title='Discriminant')}}:</td>
+	<td>$(\Delta)$</td>
+	<td>=</td>
         <td>{{ ec.disc }}</td>
         {% if ec.fact_disc %}
         <td>=</td>
@@ -102,6 +108,8 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>
         <tr><td colspan=4 style="padding:0;">{{ place_code('disc') }}</td></tr>
         <tr>
         <td>{{KNOWL('ec.discriminant', title='Discriminant norm')}}:</td>
+	<td>$N(\Delta)$</td>
+	<td>=</td>
         <td>{{ ec.disc_norm }}</td>
         <td>=</td>
         <td>{{ ec.fact_disc_norm }}</td>
@@ -111,6 +119,8 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>
 {% if not ec.is_minimal %}
         <tr>
         <td>{{KNOWL('ec.minimal_discriminant', title='Minimal discriminant')}}:</td>
+	<td>$\frak{D}_{\mathrm{min}}$</td>
+	<td>=</td>
         <td>{{ ec.mindisc }}</td>
         {% if ec.fact_mindisc %}
         <td>=</td>
@@ -120,6 +130,8 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>
 
         <tr>
         <td>{{KNOWL('ec.minimal_discriminant', title='Minimal discriminant norm')}}:</td>
+	<td>$N(\frak{D}_{\mathrm{min}})$</td>
+	<td>=</td>
         <td>{{ ec.mindisc_norm }}</td>
         <td>=</td>
         <td>{{ ec.fact_mindisc_norm }}</td>
@@ -128,6 +140,8 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>
 
         <tr>
         <td>{{ KNOWL('ec.j_invariant','j-invariant')}}:</td>
+	<td>$j$</td>
+	<td>=</td>
         {% if ec.fact_j %}
         <td>{{ ec.j }}</td>
         <td>=</td>
@@ -140,25 +154,35 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>
 
         <tr>
         <td>{{ KNOWL('ec.endomorphism_ring', title='Endomorphism ring') }}:</td>
-        <td>{% if ec.rational_cm %} {{ ec.End }} {% else %} \(\Z\) {% endif %}</td>
-        <td colspan="2">{% if ec.rational_cm %} ({{ KNOWL('ec.complex_multiplication', title='complex multiplication')}}) {% endif %}</td>
+	<td>$\mathrm{End}(E)$</td>
+	<td>=</td>
+        <td colspan="3">
+	  {% if ec.rational_cm %} {{ ec.End }} {% else %} \(\Z\) {% endif %}
+	  &nbsp;&nbsp;
+          {% if ec.rational_cm %} ({{ KNOWL('ec.complex_multiplication', title='complex multiplication')}}) {% endif %}
+	</td>
         </tr>
         
         <tr>
         <td>{{ KNOWL('ec.geom_endomorphism_ring', title='Geometric endomorphism ring') }}:</td>
-        <td>{{ ec.End }}</td>
-        <td colspan="2">
-        {%if not ec.cm %}
+	<td>$\mathrm{End}(E_{\overline{\Q}})$</td>
+	<td>=</td>
+        <td colspan="3">
+	  {{ ec.End }}
+	  &nbsp;&nbsp;
+          {%if not ec.cm %}
           (no {{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}})
-        {% elif not ec.rational_cm %}
+          {% elif not ec.rational_cm %}
           ({{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}})
-        {% endif %}
+          {% endif %}
         </td>
         </tr>
 
         <tr><td colspan=4 style="padding:0;">{{ place_code('cm') }}</td></tr>
         <tr>
         <td>{{ KNOWL('st_group.definition', title='Sato-Tate group') }}:</td>
+	<td>$\mathrm{ST}(E)$</td>
+	<td>=</td>
         <td>{{ ec.ST|safe }}</td>
         </td>
         </tr>
@@ -175,9 +199,13 @@ <h2> {{ KNOWL('ec.mordell_weil_group', title="Mordell-Weil group") }} </h2>
 {% if ec.rank_bounds != "not available" %}
   <td>\({{ ec.rk_lb }} \le r \le {{ec.rk_ub}}\)</td>
 {% else %}
+  <td>$r$</td>
+  <td>&nbsp;</td>
   <td>not available</td>
 {% endif %}
 {% else %}
+  <td>$r$</td>
+  <td>=</td>
   <td>\({{ ec.rank }}\)</td>
 {% endif %}
 </tr>
@@ -186,14 +214,15 @@ <h2> {{ KNOWL('ec.mordell_weil_group', title="Mordell-Weil group") }} </h2>
 <tr>
   <td align = 'left'>
     {% if ec.ngens==1 %}
-    {{KNOWL('ec.mw_generators','Generator')}}
+    {{KNOWL('ec.mw_generators','Non-torsion generator')}}:
     {% else %}
-    {{KNOWL('ec.mw_generators','Generators')}}
+    {{KNOWL('ec.mw_generators','Non-torsion generators')}}:
     {% endif %}
   </td>
   {% if ec.gens == 'not available' %}
   <td>not available</td>
   {% else %}
+  <td>$P$</td><td>=</td>
   {% for gen in ec.gens %}
   <td>{{ gen }}</td>
   {% endfor %}
@@ -205,11 +234,12 @@ <h2> {{ KNOWL('ec.mordell_weil_group', title="Mordell-Weil group") }} </h2>
 <tr>
   <td align = 'left'>
     {% if ec.ngens==1 %}
-    {{ KNOWL('ec.canonical_height', title="Height") }}
+    {{ KNOWL('ec.canonical_height', title="Height") }}:
     {% else %}
-    {{ KNOWL('ec.canonical_height', title="Heights") }}
+    {{ KNOWL('ec.canonical_height', title="Heights") }}:
     {% endif %}
   </td>
+  <td>$\hat{h}(P)$</td><td>&approx;</td>
   {% for h in ec.heights %}
   <td>\({{ h }}\)</td>
   {% endfor %}
@@ -218,13 +248,17 @@ <h2> {{ KNOWL('ec.mordell_weil_group', title="Mordell-Weil group") }} </h2>
 
 <tr>
 <td align='left'>{{KNOWL('ec.torsion_subgroup','Torsion structure')}}:</td>
+  <td>$E(K)_{\mathrm{tor}}$</td>
+  <td>$\cong$</td>
 <td>{{ ec.tor_struct_pretty }}</td>
 </tr>
 <tr><td colspan=2> {{ place_code('tors') }}</td></tr>
 <!-- <tr><td colspan=2> {{ place_code('ntors') }}</td></tr> -->
     {% if ec.tr %}
 <tr>
-<td align='left'>{% if ec.tr==1 %}{{KNOWL('ec.mw_generators','Torsion generator')}}{% else %}{{KNOWL('ec.mw_generators','Torsion generators')}}{% endif %}:</td>
+  <td align='left'>{% if ec.tr==1 %}{{KNOWL('ec.mw_generators','Torsion generator')}}{% else %}{{KNOWL('ec.mw_generators','Torsion generators')}}{% endif %}:</td>
+  <td>$T$</td>
+  <td>=</td>
 {% for gen in ec.torsion_gens %}
 <td>{{ gen }}</td>
 {% endfor %}
@@ -242,6 +276,7 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 
         <tr>
         <td align='left'>{{ KNOWL('lfunction.analytic_rank', title='Analytic rank') }}:</td>
+	<td>$r_{\mathrm{an}}$</td><td>=</td>
         <td>
 	  {{ ec.ar }}
         </td>
@@ -256,12 +291,16 @@ <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>&nbsp;</td>
 	  {% if ec.rank_bounds != "not available" %}
 	  <td>\({{ ec.rk_lb }} \le r \le {{ec.rk_ub}}\)</td>
 	  {% else %}
 	  <td>not available</td>
 	  {% endif %}
 	  {% else %}
+	  <td>$r$</td>
+	  <td>=</td>
 	  <td>\({{ ec.rank }}\)</td>
 	  {% endif %}
 	</tr>
@@ -273,6 +312,8 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 	    {{ KNOWL('ec.regulator', title='Regulator') }}:
 	    {% endif %}
 	  </td>
+	  <td>$\mathrm{Reg}(E/K)$</td>
+	  <td>{% if ec.rk == 0 %}={% else %}&approx;{% endif %}</td>
           <td>
 	  {% if ec.reg=='not available' %}
 	  not available
@@ -284,11 +325,13 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 
         <tr>
         <td align='left'>{{ KNOWL('ec.period', title='Period') }}:</td>
+	<td>$\Omega(E/K)$</td><td>&approx;</td>
         <td> {{ ec.omega }}</td>
         </tr>
 
         <tr>
         <td align='left'>{{ KNOWL('ec.tamagawa_number', title='Tamagawa product') }}:</td>
+	<td>$\prod_{\frak{p}}c_{\frak{p}}$</td><td>=</td>
         <td> {{ ec.tamagawa_product }}
           {% if ec.tamagawa_factors %}
           &nbsp;=&nbsp; \({{ ec.tamagawa_factors }}\)
@@ -298,18 +341,18 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 
         <tr>
         <td align='left'>{{ KNOWL('ec.torsion_order', title='Torsion order') }}:</td>
+	<td>$E(K)_{\mathrm{tors}}$</td><td>=</td>
         <td>\({{ ec.torsion_order }}\)</td>
         </tr>
 
         <tr>
         <td align='left'>{{ KNOWL('lfunction.leading_coeff', title='Leading coefficient') }}:</td>
-        <td>
-	  {% if ec.Lvalue=='not available' %}
-	  not available
-	  {% else %}
-	  {{ ec.Lvalue }}
-	  {% endif %}
-	</td>
+	<td>$L^{(r)}(E/K,1)/r!$</td>
+	{% if ec.Lvalue=='not available' %}
+	<td></td><td>not available</td>
+	{% else %}
+	<td>&approx;</td><td>{{ ec.Lvalue }}</td>
+	{% endif %}
         </tr>
 
         <tr>
@@ -320,7 +363,8 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
 	    {{ KNOWL('ec.analytic_sha_order', title='Analytic order of &#1064;') }}:
 	    {% endif %}
 	  </td>
-        <td> {{ ec.sha }} </td>
+	  <td>&#1064;${}_{\mathrm{an}}$</td><td>=</td>
+          <td> {{ ec.sha }} </td>
         </tr>
         </table>
     </p>
diff --git a/lmfdb/elliptic_curves/templates/congruent_number_data.html b/lmfdb/elliptic_curves/templates/congruent_number_data.html
index 8442566210..791199b6b4 100644
--- a/lmfdb/elliptic_curves/templates/congruent_number_data.html
+++ b/lmfdb/elliptic_curves/templates/congruent_number_data.html
@@ -119,7 +119,7 @@ <h2>Data files</h2>
       </form>
     </td>
     <td>
-      {{ KNOWL('ec.q.canonical_height', 'Heights') }}
+      {{ KNOWL('ec.canonical_height', 'Heights') }}
     </td>
     <td>
     <pre>000137    [8.4621365965410101565417149184287484305,10.575571190572966907642306531966335545]</pre>
diff --git a/lmfdb/elliptic_curves/templates/ec-curve.html b/lmfdb/elliptic_curves/templates/ec-curve.html
index 74638e324b..fbecf34b2e 100644
--- a/lmfdb/elliptic_curves/templates/ec-curve.html
+++ b/lmfdb/elliptic_curves/templates/ec-curve.html
@@ -104,9 +104,9 @@ <h2> {{ KNOWL('ec.mordell_weil_group', title='Mordell-Weil group') }} structure<
 
     {% if data.mwbsd.rank!=0 %}
     {% if data.mwbsd.rank==1 %}
-    <h3> Infinite order Mordell-Weil generator and {{KNOWL('ec.q.canonical_height','height')}}</h3>
+    <h3> {{ KNOWL('ec.mw_generators', title='Non-torsion Mordell-Weil generator') }} and {{KNOWL('ec.canonical_height','height')}}</h3>
     {% else %}
-    <h3> Infinite order Mordell-Weil generators and {{KNOWL('ec.q.canonical_height','heights')}}</h3>
+    <h3> {{ KNOWL('ec.mw_generators', title='Non-torsion Mordell-Weil generators') }} and {{KNOWL('ec.canonical_height','heights')}}</h3>
     {% endif %}
       {% if data.mwbsd.ngens==0 %}
     No {% if data.mwbsd.rank==1 %} generator {% else %} generators  {% endif %} computed
@@ -130,7 +130,7 @@ <h3> Infinite order Mordell-Weil generators and {{KNOWL('ec.q.canonical_height',
     {%endif%}
 
     {% if data.mwbsd.torsion!=1 %}
-    <h2> {{ KNOWL('ec.torsion_subgroup', title='Torsion generators') }}</h2>
+    <h2> {{ KNOWL('ec.mw_generators', title='Torsion generators') }}</h2>
     <p> {{ data.mwbsd.tor_gens |safe }} </p>
       {{ place_code('tors') }}
     {%endif %}
@@ -183,13 +183,15 @@ <h2> Invariants </h2>
 
         <tr>
         <td>{{ KNOWL('ec.geom_endomorphism_ring', title='Geometric endomorphism ring') }}:</td>
-        <td>$\mathrm{End}(E_{\overline{\Q}})$</td><td>&nbsp;=&nbsp;</td>
+        <td>$\mathrm{End}(E_{\overline{\Q}})$</td>
+	<td>&nbsp;=&nbsp;</td>
 	<td colspan=3>{{ data.data.EndE }}
-        {%if not data.data.CMD %}
-        &nbsp;&nbsp;(no {{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}})
-        {% else %}
-        &nbsp;&nbsp;({{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}})
-        {% endif %}
+	  &nbsp;&nbsp;
+          {%if not data.data.CMD %}
+          (no {{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}})
+          {% else %}
+          ({{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}})
+          {% endif %}
         </td>
         <td>{{ place_code('cm') }}</td>
         </tr>

{{KNOWL('ec.conductor', title='Conductor')}}:	$\frak{n}$	=	{{ ec.cond }}	=	{{ ec.fact_cond }}
{{KNOWL('ec.conductor', title='Conductor norm')}}:	$N(\frak{n})$	=	{{ ec.cond_norm }}	=	{{ ec.fact_cond_norm }}
{{KNOWL('ec.discriminant', title='Discriminant')}}:	$(\Delta)$	=	{{ ec.disc }}	=
{{ place_code('disc') }}
{{KNOWL('ec.discriminant', title='Discriminant norm')}}:	$N(\Delta)$	=	{{ ec.disc_norm }}	=	{{ ec.fact_disc_norm }}
{{KNOWL('ec.minimal_discriminant', title='Minimal discriminant')}}:	$\frak{D}_{\mathrm{min}}$	=	{{ ec.mindisc }}	=
{{KNOWL('ec.minimal_discriminant', title='Minimal discriminant norm')}}:	$N(\frak{D}_{\mathrm{min}})$	=	{{ ec.mindisc_norm }}	=	{{ ec.fact_mindisc_norm }}
{{ KNOWL('ec.j_invariant','j-invariant')}}:	$j$	=	{{ ec.j }}	=
{{ KNOWL('ec.endomorphism_ring', title='Endomorphism ring') }}:	{% if ec.rational_cm %} {{ ec.End }} {% else %} \(\Z\) {% endif %}	{% if ec.rational_cm %} ({{ KNOWL('ec.complex_multiplication', title='complex multiplication')}}) {% endif %}		$\mathrm{End}(E)$	=	+ {% if ec.rational_cm %} {{ ec.End }} {% else %} \(\Z\) {% endif %} + + {% if ec.rational_cm %} ({{ KNOWL('ec.complex_multiplication', title='complex multiplication')}}) {% endif %} +
{{ KNOWL('ec.geom_endomorphism_ring', title='Geometric endomorphism ring') }}:	{{ ec.End }}	- {%if not ec.cm %} +		$\mathrm{End}(E_{\overline{\Q}})$	=	+ {{ ec.End }} + + {%if not ec.cm %} (no {{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}}) - {% elif not ec.rational_cm %} + {% elif not ec.rational_cm %} ({{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}}) - {% endif %} + {% endif %}
{{ place_code('cm') }}
{{ KNOWL('st_group.definition', title='Sato-Tate group') }}:	$\mathrm{ST}(E)$	=	{{ ec.ST\|safe }}
\({{ ec.rk_lb }} \le r \le {{ec.rk_ub}}\)	$r$		not available	$r$	=	\({{ ec.rank }}\)
{% if ec.ngens==1 %} - {{KNOWL('ec.mw_generators','Generator')}} + {{KNOWL('ec.mw_generators','Non-torsion generator')}}: {% else %} - {{KNOWL('ec.mw_generators','Generators')}} + {{KNOWL('ec.mw_generators','Non-torsion generators')}}: {% endif %}	not available	$P$	=	{{ gen }}
{% if ec.ngens==1 %} - {{ KNOWL('ec.canonical_height', title="Height") }} + {{ KNOWL('ec.canonical_height', title="Height") }}: {% else %} - {{ KNOWL('ec.canonical_height', title="Heights") }} + {{ KNOWL('ec.canonical_height', title="Heights") }}: {% endif %}	$\hat{h}(P)$	≈	\({{ h }}\)
{{KNOWL('ec.torsion_subgroup','Torsion structure')}}:	$E(K)_{\mathrm{tor}}$	$\cong$	{{ ec.tor_struct_pretty }}
{{ place_code('tors') }}
{% if ec.tr==1 %}{{KNOWL('ec.mw_generators','Torsion generator')}}{% else %}{{KNOWL('ec.mw_generators','Torsion generators')}}{% endif %}:	{% if ec.tr==1 %}{{KNOWL('ec.mw_generators','Torsion generator')}}{% else %}{{KNOWL('ec.mw_generators','Torsion generators')}}{% endif %}:	$T$	=	{{ gen }}
{{ KNOWL('lfunction.analytic_rank', title='Analytic rank') }}:	$r_{\mathrm{an}}$	=	{{ ec.ar }}
{{ KNOWL('ec.rank', title="Mordell-Weil rank")}}:	$r$?		\({{ ec.rk_lb }} \le r \le {{ec.rk_ub}}\)	not available	$r$	=	\({{ ec.rank }}\)
$\mathrm{Reg}(E/K)$	{% if ec.rk == 0 %}={% else %}≈{% endif %}	{% if ec.reg=='not available' %} not available @@ -284,11 +325,13 @@ {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}
{{ KNOWL('ec.period', title='Period') }}:	$\Omega(E/K)$	≈	{{ ec.omega }}
{{ KNOWL('ec.tamagawa_number', title='Tamagawa product') }}:	$\prod_{\frak{p}}c_{\frak{p}}$	=	{{ ec.tamagawa_product }} {% if ec.tamagawa_factors %} = \({{ ec.tamagawa_factors }}\) @@ -298,18 +341,18 @@ {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}
{{ KNOWL('ec.torsion_order', title='Torsion order') }}:	$E(K)_{\mathrm{tors}}$	=	\({{ ec.torsion_order }}\)
{{ KNOWL('lfunction.leading_coeff', title='Leading coefficient') }}:	- {% if ec.Lvalue=='not available' %} - not available - {% else %} - {{ ec.Lvalue }} - {% endif %} -	$L^{(r)}(E/K,1)/r!$		not available	≈	{{ ec.Lvalue }}
{{ ec.sha }}	Ш${}_{\mathrm{an}}$	=	{{ ec.sha }}