def render_isogeny_class(iso_class):
info = {}
credit = 'John Cremona'
label = iso_class
C = base.getDBConnection()
data = C.ellcurves.isogeny.find_one({'label': label})
if data is None:
return "No such isogeny class"
ainvs = [int(a) for a in data['ainvs_for_optimal_curve']]
E = EllipticCurve(ainvs)
info = {'label': label}
info['optimal_ainvs'] = ainvs
if 'imag' in data:
info['imag'] = data['imag']
if 'real' in data:
info['real'] = data['real']
info['rank'] = data['rank']
info['isogeny_matrix'] = latex(matrix(eval(data['isogeny_matrix'])))
info['modular_degree'] = data['degree']
#info['f'] = ajax_more(E.q_eigenform, 10, 20, 50, 100, 250)
info['f'] = web_latex(E.q_eigenform(10))
G = E.isogeny_graph()
n = G.num_verts()
G.relabel(range(1, n + 1)) # proper cremona labels...
info['graph_img'] = image_src(G.plot(edge_labels=True))
curves = data['label_of_curves_in_the_class']
info['curves'] = list(curves)
info['download_qexp_url'] = url_for('download_qexp',
limit=100,
ainvs=','.join([str(a)
for a in ainvs]))
info['download_all_url'] = url_for('download_all', label=str(label))
friends = [('Elliptic Curve %s' % l, "/EllipticCurve/Q/%s" % l)
for l in data['label_of_curves_in_the_class']]
friends.append(('Quadratic Twist', "/quadratic_twists/%s" % (label)))
friends.append(('Modular Form',
url_for("emf.render_classical_modular_form_from_label",
label="%s" % (label))))
info['friends'] = friends
t = "Elliptic Curve Isogeny Class %s" % info['label']
bread = [('Elliptic Curves ', url_for("rational_elliptic_curves")),
('isogeny class %s' % info['label'], ' ')]
return render_template("elliptic_curve/iso_class.html",
info=info,
bread=bread,
credit=credit,
title=t)
def plot_iso_graph(label):
C = lmfdb.base.getDBConnection()
data = C.elliptic_curves.curves.find_one({'lmfdb_iso': label})
if data is None:
return elliptic_curve_jump_error(label, {})
ainvs = [int(a) for a in data['ainvs']]
E = EllipticCurve(ainvs)
G = E.isogeny_graph()
n = G.num_verts()
P = G.plot(edge_labels=True, layout='spring')
_, filename = tempfile.mkstemp('.png')
P.save(filename)
data = open(filename).read()
os.unlink(filename)
response = make_response(data)
response.headers['Content-type'] = 'image/png'
return response
def plot_iso_graph(label):
C = lmfdb.base.getDBConnection()
data = C.elliptic_curves.curves.find_one({'lmfdb_iso': label})
if data is None:
return elliptic_curve_jump_error(label, {})
ainvs = [int(a) for a in data['ainvs']]
E = EllipticCurve(ainvs)
G = E.isogeny_graph()
n = G.num_verts()
P = G.plot(edge_labels=True, layout='spring')
_, filename = tempfile.mkstemp('.png')
P.save(filename)
data = open(filename).read()
os.unlink(filename)
response = make_response(data)
response.headers['Content-type'] = 'image/png'
return response
def plot_iso_graph(label):
C = lmfdb.base.getDBConnection()
data = C.elliptic_curves.curves.find_one({"lmfdb_iso": label})
if data is None:
return elliptic_curve_jump_error(label, {})
ainvs = [int(a) for a in data["ainvs"]]
E = EllipticCurve(ainvs)
G = E.isogeny_graph()
n = G.num_verts()
G.relabel(range(1, n + 1)) # proper lmfdb labels...
P = G.plot(edge_labels=True, layout="spring")
_, filename = tempfile.mkstemp(".png")
P.save(filename)
data = open(filename).read()
os.unlink(filename)
response = make_response(data)
response.headers["Content-type"] = "image/png"
return response
def render_isogeny_class(iso_class):
info = {}
credit = 'John Cremona'
label=iso_class
C = base.getDBConnection()
data = C.ellcurves.isogeny.find_one({'label': label})
if data is None:
return "No such isogeny class"
ainvs = [int(a) for a in data['ainvs_for_optimal_curve']]
E = EllipticCurve(ainvs)
info = {'label': label}
info['optimal_ainvs'] = ainvs
if 'imag' in data:
info['imag']=data['imag']
if 'real' in data:
info['real']=data['real']
info['rank'] = data['rank']
info['isogeny_matrix']=latex(matrix(eval(data['isogeny_matrix'])))
info['modular_degree']=data['degree']
#info['f'] = ajax_more(E.q_eigenform, 10, 20, 50, 100, 250)
info['f'] = web_latex(E.q_eigenform(10))
G = E.isogeny_graph(); n = G.num_verts()
G.relabel(range(1,n+1)) # proper cremona labels...
info['graph_img'] = image_src(G.plot(edge_labels=True))
curves = data['label_of_curves_in_the_class']
info['curves'] = list(curves)
info['download_qexp_url'] = url_for('download_qexp', limit=100, ainvs=','.join([str(a) for a in ainvs]))
info['download_all_url'] = url_for('download_all', label=str(label))
friends=[('Elliptic Curve %s' % l , "/EllipticCurve/Q/%s" % l) for l in data['label_of_curves_in_the_class']]
friends.append(('Quadratic Twist', "/quadratic_twists/%s" % (label)))
friends.append(('Modular Form', url_for("emf.render_classical_modular_form_from_label",label="%s" %(label))))
info['friends'] = friends
t= "Elliptic Curve Isogeny Class %s" % info['label']
bread = [('Elliptic Curves ', url_for("rational_elliptic_curves")),('isogeny class %s' %info['label'],' ')]
return render_template("elliptic_curve/iso_class.html", info = info,bread=bread, credit=credit,title = t)
