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EC/ECNF consistency in local data display #6287

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merged 2 commits into from
Dec 6, 2024
Merged

EC/ECNF consistency in local data display #6287

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b64f1d2
EC/ECNF consistency in local data display
JohnCremona Dec 4, 2024
d4962b1
ECNF local info tweaks and improved discriminant display and knowls
JohnCremona Dec 6, 2024
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3 changes: 3 additions & 0 deletions lmfdb/ecnf/WebEllipticCurve.py
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Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand Down
73 changes: 59 additions & 14 deletions lmfdb/ecnf/templates/ecnf-curve.html
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Original file line number Diff line number Diff line change
Expand Up @@ -107,7 +107,7 @@ <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>$\frak{N}$</td>
<td>=</td>
<td>{{ ec.cond }}</td>
<td>=</td>
Expand All @@ -117,7 +117,7 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>

<tr>
<td>{{KNOWL('ec.conductor', title='Conductor norm')}}:</td>
<td>$N(\frak{n})$</td>
<td>$N(\frak{N})$</td>
<td>=</td>
<td>{{ ec.cond_norm }}</td>
<td>=</td>
Expand All @@ -127,7 +127,26 @@ <h2>{{ KNOWL('ec.invariants', title='Invariants')}}</h2>

<tr>
<td>{{KNOWL('ec.discriminant', title='Discriminant')}}:</td>
<td>$(\Delta)$</td>
<td>$\Delta$</td>
<td>=</td>
<td>${{ ec.model_disc }}$</td>
</tr>

<tr>
<td>
{% if ec.is_minimal %}
{{KNOWL('ec.minimal_discriminant', title='Discriminant ideal')}}:
{% else %}
{{KNOWL('ec.discriminant', title='Discriminant ideal')}}:
{% endif %}
</td>
<td>
{% if ec.is_minimal %}
$\frak{D}_{\mathrm{min}} = (\Delta)$
{% else %}
$(\Delta)$
{% endif %}
</td>
<td>=</td>
<td>{{ ec.disc }}</td>
{% if ec.fact_disc %}
Expand All @@ -138,8 +157,20 @@ <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>
{% if ec.is_minimal %}
{{KNOWL('ec.minimal_discriminant', title='Discriminant norm')}}:
{% else %}
{{KNOWL('ec.discriminant', title='Discriminant norm')}}:
{% endif %}
</td>
<td>
{% if ec.is_minimal %}
$N(\frak{D}_{\mathrm{min}}) = N(\Delta)$
{% else %}
$N(\Delta)$
{% endif %}
</td>
<td>=</td>
<td>{{ ec.disc_norm }}</td>
<td>=</td>
Expand Down Expand Up @@ -276,7 +307,7 @@ <h2> {{ KNOWL('ec.bsdconjecture', title='BSD invariants') }}</h2>
</tr>

<tr>
<td align='left'>{{ KNOWL('ec.period', title='Period') }}:</td>
<td align='left'>{{ KNOWL('ec.period', title='Global period') }}:</td>
<td>$\Omega(E/K)$</td><td>&approx;</td>
<td> {{ ec.omega }}</td>
</tr>
Expand Down Expand Up @@ -341,25 +372,41 @@ <h2>{{KNOWL('ec.local_data', title='Local data')}} at {{KNOWL('ec.bad_reduction'
<div>
{{ place_code('localdata') }}

<p>
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 %}
</p>


{% if ec.local_data %}
<table class="ntdata"><thead>
<table class="ntdata centered"><thead>
<tr>
<th>prime</th>
<th>Norm</th>
<th>$\mathfrak{p}$</th>
<th>$N(\mathfrak{p})$</th>
<th>{{KNOWL('ec.tamagawa_number', title='Tamagawa number')}}</th>
<th>{{KNOWL('ec.kodaira_symbol', title='Kodaira symbol')}}</th>
<th>{{KNOWL('ec.reduction_type', title='Reduction type')}}</th>
{% if ec.local_data.0.rootno %}
<th>{{KNOWL('ec.local_root_number', title='Root number')}}</th>
{% endif %}
<th>{{KNOWL('ec.conductor_valuation', title='ord(\(\mathfrak{N}\))')}}</th>
<th>{{KNOWL('ec.discriminant_valuation', title='ord(\(\mathfrak{D}\))')}}</th>
<th>{{KNOWL('ec.j_invariant_denominator_valuation', title='ord\((j)_{-}\)')}}</th>
<th>{{KNOWL('ec.conductor_valuation', title='\(\mathrm{ord}_{\mathfrak{p}}(\mathfrak{N}\))')}}</th>
<th>{{KNOWL('ec.discriminant_valuation', title='\(\mathrm{ord}_{\mathfrak{p}}(\mathfrak{D}_{\mathrm{min}}\))')}}</th>
<th>{{KNOWL('ec.j_invariant_denominator_valuation', title='\(\mathrm{ord}_{\mathfrak{p}}(\mathrm{den}(j))\)')}}</th>
</tr>
</thead><tbody>
{% for pr in ec.local_data %}
Expand Down Expand Up @@ -397,8 +444,6 @@ <h2>{{KNOWL('ec.local_data', title='Local data')}} at {{KNOWL('ec.bad_reduction'
{% endfor %}
</tbody>
</table>
{% else %}
No primes of bad reduction.
{% endif %}
</div>

Expand Down
8 changes: 4 additions & 4 deletions lmfdb/elliptic_curves/templates/ec-curve.html
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Original file line number Diff line number Diff line change
Expand Up @@ -406,7 +406,7 @@ <h4> {{ KNOWL('ec.q.modular_degree', title='Modular degree') }}
{% endif %}
</p>

<h2> Local data </h2>
<h2>{{KNOWL('ec.local_data', title='Local data')}} at {{KNOWL('ec.bad_reduction', title='primes of bad reduction')}} </h2>

<style type="text/css">
#local_data th, #local_data td, #serre_data th, #serre_data td {
Expand All @@ -433,9 +433,9 @@ <h2> Local data </h2>
<th>{{KNOWL('ec.q.kodaira_symbol', title='Kodaira symbol')}}</th>
<th>{{KNOWL('ec.q.reduction_type', title='Reduction type')}}</th>
<th>{{KNOWL('ec.local_root_number', title='Root number')}}</th>
<th>{{KNOWL('ec.conductor_valuation', title='$v_p(N)$')}}</th>
<th>{{KNOWL('ec.discriminant_valuation', title='$v_p(\Delta)$')}}</th>
<th>{{KNOWL('ec.j_invariant_denominator_valuation', title='$v_p(\mathrm{den}(j))$')}}</th>
<th>{{KNOWL('ec.conductor_valuation', title='$\mathrm{ord}_p(N)$')}}</th>
<th>{{KNOWL('ec.discriminant_valuation', title='$\mathrm{ord}_p(\Delta)$')}}</th>
<th>{{KNOWL('ec.j_invariant_denominator_valuation', title='$\mathrm{ord}_p(\mathrm{den}(j))$')}}</th>
</tr>
</thead><tbody>
{% for pr in data.local_data %}
Expand Down
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