diff --git a/lmfdb/ecnf/WebEllipticCurve.py b/lmfdb/ecnf/WebEllipticCurve.py
index 2e86ebb890..bd8651fcc0 100644
--- a/lmfdb/ecnf/WebEllipticCurve.py
+++ b/lmfdb/ecnf/WebEllipticCurve.py
@@ -359,6 +359,9 @@ def make_E(self):
self.cond_norm = web_latex(self.conductor_norm)
Dnorm = self.normdisc
+ self.model_disc = self.disc.replace('w', Kgen).replace("*","").replace("(","").replace(")","")
+ if Kgen == 'phi':
+ self.model_disc = self.model_disc.replace(Kgen, r"\phi")
self.disc = pretty_ideal(Kgen, self.disc)
local_data = self.local_data
diff --git a/lmfdb/ecnf/templates/ecnf-curve.html b/lmfdb/ecnf/templates/ecnf-curve.html
index baed8cc381..d5a48fa4d7 100644
--- a/lmfdb/ecnf/templates/ecnf-curve.html
+++ b/lmfdb/ecnf/templates/ecnf-curve.html
@@ -107,7 +107,7 @@
{{ KNOWL('ec.invariants', title='Invariants')}}
{{KNOWL('ec.conductor', title='Conductor')}}: |
- $\frak{n}$ |
+ $\frak{N}$ |
= |
{{ ec.cond }} |
= |
@@ -117,7 +117,7 @@ {{ KNOWL('ec.invariants', title='Invariants')}}
{{KNOWL('ec.conductor', title='Conductor norm')}}: |
- $N(\frak{n})$ |
+ $N(\frak{N})$ |
= |
{{ ec.cond_norm }} |
= |
@@ -127,7 +127,26 @@ {{ KNOWL('ec.invariants', title='Invariants')}}
{{KNOWL('ec.discriminant', title='Discriminant')}}: |
- $(\Delta)$ |
+ $\Delta$ |
+ = |
+ ${{ ec.model_disc }}$ |
+
+
+
+
+ {% if ec.is_minimal %}
+ {{KNOWL('ec.minimal_discriminant', title='Discriminant ideal')}}:
+ {% else %}
+ {{KNOWL('ec.discriminant', title='Discriminant ideal')}}:
+ {% endif %}
+ |
+
+ {% if ec.is_minimal %}
+ $\frak{D}_{\mathrm{min}} = (\Delta)$
+ {% else %}
+ $(\Delta)$
+ {% endif %}
+ |
= |
{{ ec.disc }} |
{% if ec.fact_disc %}
@@ -138,8 +157,20 @@ {{ KNOWL('ec.invariants', title='Invariants')}}
{{ place_code('disc') }} |
- {{KNOWL('ec.discriminant', title='Discriminant norm')}}: |
- $N(\Delta)$ |
+
+ {% if ec.is_minimal %}
+ {{KNOWL('ec.minimal_discriminant', title='Discriminant norm')}}:
+ {% else %}
+ {{KNOWL('ec.discriminant', title='Discriminant norm')}}:
+ {% endif %}
+ |
+
+ {% if ec.is_minimal %}
+ $N(\frak{D}_{\mathrm{min}}) = N(\Delta)$
+ {% else %}
+ $N(\Delta)$
+ {% endif %}
+ |
= |
{{ ec.disc_norm }} |
= |
@@ -276,7 +307,7 @@ {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}
- {{ KNOWL('ec.period', title='Period') }}: |
+ {{ KNOWL('ec.period', title='Global period') }}: |
$\Omega(E/K)$ | ≈ |
{{ ec.omega }} |
@@ -341,25 +372,41 @@ {{KNOWL('ec.local_data', title='Local data')}} at {{KNOWL('ec.bad_reduction'
{{ place_code('localdata') }}
+
+ This elliptic curve is {{ '' if ec.semistable else 'not' }} {{KNOWL('ec.semistable', title='semistable')}}.
+ There
+ {% if ec.n_bad_primes==0 %}
+ are no primes
+ {% else %}
+ {% if ec.n_bad_primes==1 %}
+ is only one prime $\frak{p}$
+ {% else %}
+ are {{ec.n_bad_primes }} primes $\frak{p}$
+ {% endif %}
+ {% endif %}
+ of {{KNOWL('ec.q.reduction_type', title='bad reduction')}}.
+
{% if not ec.is_minimal %}
Primes of good reduction for the curve but which divide the
discriminant of the model above (if any) are included.
{% endif %}
+
+
{% if ec.local_data %}
-
+
-prime |
-Norm |
+$\mathfrak{p}$ |
+$N(\mathfrak{p})$ |
{{KNOWL('ec.tamagawa_number', title='Tamagawa number')}} |
{{KNOWL('ec.kodaira_symbol', title='Kodaira symbol')}} |
{{KNOWL('ec.reduction_type', title='Reduction type')}} |
{% if ec.local_data.0.rootno %}
{{KNOWL('ec.local_root_number', title='Root number')}} |
{% endif %}
-{{KNOWL('ec.conductor_valuation', title='ord(\(\mathfrak{N}\))')}} |
-{{KNOWL('ec.discriminant_valuation', title='ord(\(\mathfrak{D}\))')}} |
-{{KNOWL('ec.j_invariant_denominator_valuation', title='ord\((j)_{-}\)')}} |
+{{KNOWL('ec.conductor_valuation', title='\(\mathrm{ord}_{\mathfrak{p}}(\mathfrak{N}\))')}} |
+{{KNOWL('ec.discriminant_valuation', title='\(\mathrm{ord}_{\mathfrak{p}}(\mathfrak{D}_{\mathrm{min}}\))')}} |
+{{KNOWL('ec.j_invariant_denominator_valuation', title='\(\mathrm{ord}_{\mathfrak{p}}(\mathrm{den}(j))\)')}} |
{% for pr in ec.local_data %}
@@ -397,8 +444,6 @@ {{KNOWL('ec.local_data', title='Local data')}} at {{KNOWL('ec.bad_reduction'
{% endfor %}
-{% else %}
-No primes of bad reduction.
{% endif %}
diff --git a/lmfdb/elliptic_curves/templates/ec-curve.html b/lmfdb/elliptic_curves/templates/ec-curve.html
index e49ec675c7..78c1c9fa1a 100644
--- a/lmfdb/elliptic_curves/templates/ec-curve.html
+++ b/lmfdb/elliptic_curves/templates/ec-curve.html
@@ -406,7 +406,7 @@ {{ KNOWL('ec.q.modular_degree', title='Modular degree') }}
{% endif %}
- Local data
+{{KNOWL('ec.local_data', title='Local data')}} at {{KNOWL('ec.bad_reduction', title='primes of bad reduction')}}