From 06ecfe6dce1fa17aa6aee25c781097db18ca1dd7 Mon Sep 17 00:00:00 2001 From: John Cremona Date: Mon, 18 Nov 2024 09:41:28 -0500 Subject: [PATCH] fixes for issue #4943 --- lmfdb/elliptic_curves/templates/ec-curve.html | 55 ++++++++----------- 1 file changed, 24 insertions(+), 31 deletions(-) diff --git a/lmfdb/elliptic_curves/templates/ec-curve.html b/lmfdb/elliptic_curves/templates/ec-curve.html index ad273bdc60..96cb60ffed 100644 --- a/lmfdb/elliptic_curves/templates/ec-curve.html +++ b/lmfdb/elliptic_curves/templates/ec-curve.html @@ -178,20 +178,20 @@

Invariants

{{ KNOWL('ec.endomorphism_ring', title='Endomorphism ring') }}: - $\Z$ + $\mathrm{End}(E)$ = $\Z$ {{ KNOWL('ec.geom_endomorphism_ring', title='Geometric endomorphism ring') }}: - {{ data.data.EndE }} - + $\mathrm{End}(E_{\overline{\Q}})$ =  + {{ data.data.EndE }} {%if not data.data.CMD %} - (no {{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}}) +   (no {{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}}) {% else %} - ({{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}}) +   ({{ KNOWL('ec.complex_multiplication', title='potential complex multiplication')}}) {% endif %} - {{ place_code('cm') }} + {{ place_code('cm') }} @@ -201,29 +201,27 @@

Invariants

{{ KNOWL('ec.q.faltings_height', title='Faltings height') }}: - ${{ data.faltings_height }}\dots$ - + $h_{\mathrm{Faltings}}$ ≈ ${{ data.faltings_height }}$ {{ place_code('faltings') }} {{ KNOWL('ec.q.faltings_height', title='Stable Faltings height') }}: - ${{ data.stable_faltings_height }}\dots$ - + $h_{\mathrm{stable}}$ ≈ ${{ data.stable_faltings_height }}$ {{ place_code('stable_faltings') }} {{ KNOWL('ec.q.abc_quality', title='$abc$ quality') }}: - ${{ data.abc_quality }}\dots$ - + $Q$ ≈ ${{ data.abc_quality }}$ + {{ place_code('abc_quality') }} {{ KNOWL('ec.q.szpiro_ratio', title='Szpiro ratio') }}: - ${{ data.szpiro_ratio }}\dots$ - + $\sigma_{m}$ ≈ ${{ data.szpiro_ratio }}$ + {{ place_code('szpiro_ratio') }} @@ -234,7 +232,7 @@

{{ KNOWL('ec.q.bsdconjecture', title='BSD invariants') }}

{{ KNOWL('ec.q.analytic_rank', title='Analytic rank') }}: - ${{ data.analytic_rank }}$ + $r_{\mathrm{an}}$ = $ {{ data.analytic_rank }}$ {{ place_code('analytic_rank') }} @@ -245,9 +243,9 @@

{{ KNOWL('ec.q.bsdconjecture', title='BSD invariants') }}

Not computed {% else %} {% if data.rank==0 %} - $1$ + $\mathrm{Reg}(E/\Q)$ = $1$ {% else %} - ${{ data.mwbsd.reg }}\dots$ + $\mathrm{Reg}(E/\Q)$ ≈ ${{ data.mwbsd.reg }}$ {% endif %} {% endif %} {{ place_code('reg') }} @@ -255,13 +253,13 @@

{{ KNOWL('ec.q.bsdconjecture', title='BSD invariants') }}

{{ KNOWL('ec.q.real_period', title='Real period') }}: - ${{ data.mwbsd.real_period }}\dots$ + $\Omega$ ≈ ${{ data.mwbsd.real_period }}$ {{ place_code('real_period') }} {{ KNOWL('ec.tamagawa_number', title='Tamagawa product') }}: - $ {{ data.mwbsd.tamagawa_product }} $ + $\prod_{p}c_p$ = $ {{ data.mwbsd.tamagawa_product }} $ {% if data.mwbsd.tamagawa_factors %}  = $ {{ data.mwbsd.tamagawa_factors }} $ {% endif %} @@ -271,24 +269,19 @@

{{ KNOWL('ec.q.bsdconjecture', title='BSD invariants') }}

{{ KNOWL('ec.torsion_order', title='Torsion order') }}: - ${{ data.mwbsd.torsion }}$ + $E(\Q)_{\mathrm{tors}}$ = ${{ data.mwbsd.torsion }}$ {{ place_code('ntors') }} {{ KNOWL('ec.analytic_sha_order', title='Analytic order of Ш') }}: - - {% if data.mwbsd.sha == '?' %} - Not computed - {% else %} - ${{data.mwbsd.sha }}$ - {% if data.mwbsd.sha > 1 %} - = {{data.mwbsd.sha2}} - {% endif %} + {% if data.mwbsd.sha == '?' %}Not computed{% else %} Ш${}_{\mathrm{an}}$ + {% if data.mwbsd.sha_is_exact %} = {% else %} ≈ {% endif %} + ${{data.mwbsd.sha }}$ {% if data.mwbsd.sha > 1 %} = {{data.mwbsd.sha2}} {% endif %}   {% if data.mwbsd.sha_is_exact %} - ({{ KNOWL('ec.analytic_sha_value',title="exact") }}) + ({{ KNOWL('ec.q.analytic_sha_value',title="exact") }}) {% else %} - ({{ KNOWL('ec.analytic_sha_value',title="rounded") }}) + ({{ KNOWL('ec.q.analytic_sha_value',title="rounded") }}) {% endif %} {% endif %} @@ -302,7 +295,7 @@

{{ KNOWL('ec.q.bsdconjecture', title='BSD invariants') }}

{% endif %} {{KNOWL('ec.q.special_value', title='Special value', special_value = data.special_value)}}: - $ {{ data.mwbsd.lder_name }} $ ≈ $ {{ data.mwbsd.special_value }} $ + $ {{ data.mwbsd.lder_name }}$ ≈ ${{ data.mwbsd.special_value }} $ {{ place_code('L1') }}