def elliptic_curve_search(**args):
info = to_dict(args)
query = {}
bread = [('Elliptic Curves', url_for("ecnf.index")),
('$\Q$', url_for(".rational_elliptic_curves")),
('Search Results', '.')]
if 'SearchAgain' in args:
return rational_elliptic_curves()
if 'jump' in args:
label = info.get('label', '').replace(" ", "")
m = match_lmfdb_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif label.startswith("Cremona:"):
label = label[8:]
m = match_cremona_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif match_cremona_label(label):
return elliptic_curve_jump_error(label, info, cremona_label=True)
elif label:
# Try to parse a string like [1,0,3,2,4] as valid
# Weistrass coefficients:
lab = re.sub(r'\s','',label)
lab = re.sub(r'^\[','',lab)
lab = re.sub(r']$','',lab)
try:
labvec = lab.split(',')
labvec = [QQ(str(z)) for z in labvec] # Rationals allowed
E = EllipticCurve(labvec)
# Now we do have a valid curve over Q, but it might
# not be in the database.
ainvs = [str(c) for c in E.minimal_model().ainvs()]
data = db_ec().find_one({'ainvs': ainvs})
if data is None:
info['conductor'] = E.conductor()
return elliptic_curve_jump_error(label, info, missing_curve=True)
return by_ec_label(data['lmfdb_label'])
except (TypeError, ValueError, ArithmeticError):
return elliptic_curve_jump_error(label, info)
else:
query['label'] = ''
if info.get('jinv'):
j = clean_input(info['jinv'])
j = j.replace('+', '')
if not QQ_RE.match(j):
info['err'] = 'Error parsing input for the j-invariant. It needs to be a rational number.'
return search_input_error(info, bread)
query['jinv'] = str(QQ(j)) # to simplify e.g. 1728/1
for field in ['conductor', 'torsion', 'rank', 'sha']:
if info.get(field):
info[field] = clean_input(info[field])
ran = info[field]
ran = ran.replace('..', '-').replace(' ', '')
if not LIST_RE.match(ran):
names = {'conductor': 'conductor', 'torsion': 'torsion order', 'rank':
'rank', 'sha': 'analytic order of Ш'}
info['err'] = 'Error parsing input for the %s. It needs to be an integer (such as 25), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).' % names[field]
return search_input_error(info, bread)
# Past input check
tmp = parse_range2(ran, field)
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'optimal' in info and info['optimal'] == 'on':
# fails on 990h3
query['number'] = 1
if 'torsion_structure' in info and info['torsion_structure']:
res = parse_torsion_structure(info['torsion_structure'],2)
if 'Error' in res:
info['err'] = res
return search_input_error(info, bread)
#update info for repeat searches
info['torsion_structure'] = str(res).replace(' ','')
query['torsion_structure'] = [str(r) for r in res]
if info.get('surj_primes'):
info['surj_primes'] = clean_input(info['surj_primes'])
format_ok = LIST_POSINT_RE.match(info['surj_primes'])
if format_ok:
surj_primes = [int(p) for p in info['surj_primes'].split(',')]
format_ok = all([ZZ(p).is_prime(proof=False) for p in surj_primes])
if format_ok:
query['non-surjective_primes'] = {"$nin": surj_primes}
else:
info['err'] = 'Error parsing input for surjective primes. It needs to be a prime (such as 5), or a comma-separated list of primes (such as 2,3,11).'
return search_input_error(info, bread)
if info.get('nonsurj_primes'):
info['nonsurj_primes'] = clean_input(info['nonsurj_primes'])
format_ok = LIST_POSINT_RE.match(info['nonsurj_primes'])
if format_ok:
nonsurj_primes = [int(p) for p in info['nonsurj_primes'].split(',')]
format_ok = all([ZZ(p).is_prime(proof=False) for p in nonsurj_primes])
if format_ok:
if info['surj_quantifier'] == 'exactly':
nonsurj_primes.sort()
query['non-surjective_primes'] = nonsurj_primes
else:
if 'non-surjective_primes' in query:
query['non-surjective_primes'] = { "$nin": surj_primes, "$all": nonsurj_primes }
else:
query['non-surjective_primes'] = { "$all": nonsurj_primes }
else:
info['err'] = 'Error parsing input for nonsurjective primes. It needs to be a prime (such as 5), or a comma-separated list of primes (such as 2,3,11).'
return search_input_error(info, bread)
if 'download' in info and info['download'] != '0':
res = db_ec().find(query).sort([ ('conductor', ASCENDING), ('iso_nlabel', ASCENDING), ('lmfdb_number', ASCENDING) ])
return download_search(info, res)
count_default = 100
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
info['count'] = count
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if(start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
cursor = db_ec().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('conductor', ASCENDING), ('iso_nlabel', ASCENDING), ('lmfdb_number', ASCENDING)
]).skip(start).limit(count)
info['curves'] = res
info['format_ainvs'] = format_ainvs
info['curve_url'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
if nres == 1:
info['report'] = 'unique match'
elif nres == 2:
info['report'] = 'displaying both matches'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
credit = 'John Cremona'
if 'non-surjective_primes' in query:
credit += 'and Andrew Sutherland'
t = 'Elliptic Curves search results'
return render_template("search_results.html", info=info, credit=credit, bread=bread, title=t)
def genus2_curve_search(**args):
info = to_dict(args)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_dict"] = real_geom_end_alg_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
return render_curve_webpage_by_label(info["jump"])
if info.get("disc"):
field = "abs_disc"
ran = info["disc"]
ran = ran.replace('..', '-').replace(' ','')
# Past input check
dlist = parse_discs(ran)
tmp = g2_list_to_query(dlist)
if len(tmp) == 1:
tmp = tmp[0]
else:
query[tmp[0][0]] = tmp[0][1]
tmp = tmp[1]
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if info.get("is_gl2_type"):
if info['is_gl2_type'] == "True":
query['is_gl2_type']= True
elif info['is_gl2_type'] == "False":
query['is_gl2_type']= False
for fld in ['st_group', 'real_geom_end_alg']:
if info.get(fld):
query[fld] = info[fld]
for fld in ['aut_grp', 'geom_aut_grp','igusa_clebsch']:
if info.get(fld):
query[fld] = map(int,info[fld].strip()[1:-1].split(","))
if info.get('torsion'):
res = parse_torsion_structure(info['torsion'],4)
if 'Error' in res:
# no error handling of malformed input yet!
info['torsion'] = ''
#info['err'] = res
#return search_input_error(info, bread)
else:
#update info for repeat searches
info['torsion'] = str(res).replace(' ','')
query['torsion'] = [int(r) for r in res]
if info.get('ic0'):
query['igusa_clebsch']=[info['ic0'], info['ic1'], info['ic2'], info['ic3'] ]
for fld in ["cond", "num_rat_wpts", "torsion_order", "two_selmer_rank"]:
if info.get(fld):
field = fld
ran = str(info[field])
ran = ran.replace('..', '-').replace(' ','')
# Past input check
tmp = parse_range2(ran, field)
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
info["query"] = dict(query)
count_default = 50
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
info['count'] = count
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if(start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
cursor = db_g2c().curves.find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one({'label' : isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html", info=info, credit=credit, bread=bread, title=title)
def elliptic_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label.strip())
except IndexError:
if not 'query' in info:
info['query'] = {}
bread = [("Elliptic Curves", url_for(".index"))]
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
bread = [('Elliptic Curves', url_for(".index")),
('Search Results', '.')]
if 'conductor_norm' in info:
Nnorm = clean_input(info['conductor_norm'])
Nnorm = Nnorm.replace('..', '-').replace(' ', '')
tmp = parse_range2(Nnorm, 'conductor_norm')
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'conductor_label' in info:
query['conductor_label'] = info['conductor_label']
deg = None
if 'field' in info:
field_label = parse_field_string(info['field'])
#print("Field label was %s; after parsing, is %s" % (info['field'], field_label))
if FIELD_LABEL_RE.match(field_label):
query['field_label'] = field_label
deg = int(field_label.split(".")[0])
else:
info['err'] = 'unrecognised field: %s' % info['field']
return search_input_error(info, bread)
if 'jinv' in info:
if deg == None:
info['err'] = 'You must specify a field when searching by j-invariant'
return search_input_error(info, bread)
else:
query['jinv'] = pol_string_to_j_list(info['jinv'], deg=deg)
if info.get('torsion'):
ran = info['torsion'] = clean_input(info['torsion'])
ran = ran.replace('..', '-').replace(' ', '')
if not LIST_RE.match(ran):
info['err'] = 'Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).'
return search_input_error(info, bread)
# Past input check
tmp = parse_range2(ran, 'torsion_order')
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'torsion_structure' in info and info['torsion_structure']:
res = parse_torsion_structure(info['torsion_structure'],2)
if 'Error' in res:
info['err'] = res
return search_input_error(info, bread)
#update info for repeat searches
info['torsion_structure'] = str(res).replace(' ','')
query['torsion_structure'] = [int(r) for r in res]
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
info['number'] = 1
query['number'] = 1
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['base_change'] = []
else:
info['include_base_change'] = "on"
info['query'] = query
# process count and start if not default:
count_default = 50
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if(start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_nlabel', ASC), ('number', ASC)]).skip(start).limit(count)
res = list(res)
for e in res:
e['numb'] = str(e['number'])
e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), e['field_label'])
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curve search results'
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def elliptic_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label.strip())
except IndexError:
if not 'query' in info:
info['query'] = {}
bread = [("Elliptic Curves", url_for(".index"))]
info[
'err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
bread = [('Elliptic Curves', url_for(".index")), ('Search Results', '.')]
if 'conductor_norm' in info:
Nnorm = clean_input(info['conductor_norm'])
Nnorm = Nnorm.replace('..', '-').replace(' ', '')
tmp = parse_range2(Nnorm, 'conductor_norm')
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'conductor_label' in info:
query['conductor_label'] = info['conductor_label']
if 'jinv' in info:
query['jinv'] = info['jinv']
if info.get('torsion'):
ran = info['torsion'] = clean_input(info['torsion'])
ran = ran.replace('..', '-').replace(' ', '')
if not LIST_RE.match(ran):
info[
'err'] = 'Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).'
return search_input_error(info, bread)
# Past input check
tmp = parse_range2(ran, 'torsion_order')
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'torsion_structure' in info and info['torsion_structure']:
res = parse_torsion_structure(info['torsion_structure'], 2)
if 'Error' in res:
info['err'] = res
return search_input_error(info, bread)
#update info for repeat searches
info['torsion_structure'] = str(res).replace(' ', '')
query['torsion_structure'] = [int(r) for r in res]
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
query['number'] = 1
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['base_change'] = []
else:
info['include_base_change'] = "on"
if 'field' in info:
query['field_label'] = parse_field_string(info['field'])
info['query'] = query
# process count and start if not default:
count_default = 50
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if (start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC),
('conductor_label', ASC), ('iso_nlabel', ASC),
('number', ASC)]).skip(start).limit(count)
res = list(res)
for e in res:
e['numb'] = str(e['number'])
e['field_knowl'] = nf_display_knowl(e['field_label'],
getDBConnection(),
e['field_label'])
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curve search results'
return render_template("ecnf-search-results.html",
info=info,
credit=ecnf_credit,
bread=bread,
title=t)
def elliptic_curve_search(**args):
info = to_dict(args["data"])
if "jump" in info:
label = info.get("label", "").replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label)
except IndexError:
if not "query" in info:
info["query"] = {}
bread = [("Elliptic Curves", url_for(".index"))]
info["err"] = "No elliptic curve in the database has label %s." % label
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
bread = [("Elliptic Curves", url_for(".index")), ("Search Results", ".")]
if "conductor_norm" in info:
Nnorm = clean_input(info["conductor_norm"])
Nnorm = Nnorm.replace("..", "-").replace(" ", "")
tmp = parse_range2(Nnorm, "conductor_norm")
if tmp[0] == "$or" and "$or" in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query["$or"]]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if "conductor_label" in info:
query["conductor_label"] = info["conductor_label"]
if "jinv" in info:
query["jinv"] = info["jinv"]
if info.get("torsion"):
ran = info["torsion"] = clean_input(info["torsion"])
ran = ran.replace("..", "-").replace(" ", "")
if not LIST_RE.match(ran):
info[
"err"
] = "Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121)."
return search_input_error(info, bread)
# Past input check
tmp = parse_range2(ran, "torsion_order")
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == "$or" and "$or" in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query["$or"]]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if "torsion_structure" in info and info["torsion_structure"]:
res = parse_torsion_structure(info["torsion_structure"], 2)
if "Error" in res:
info["err"] = res
return search_input_error(info, bread)
# update info for repeat searches
info["torsion_structure"] = str(res).replace(" ", "")
query["torsion_structure"] = [int(r) for r in res]
if "include_isogenous" in info and info["include_isogenous"] == "off":
query["number"] = 1
if "include_base_change" in info and info["include_base_change"] == "off":
query["base_change"] = []
else:
info["include_base_change"] = "on"
if "field" in info:
query["field_label"] = parse_field_string(info["field"])
info["query"] = query
# process count and start if not default:
count_default = 50
if info.get("count"):
try:
count = int(info["count"])
except:
count = count_default
else:
count = count_default
start_default = 0
if info.get("start"):
try:
start = int(info["start"])
if start < 0:
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if start >= nres:
start -= (1 + (start - nres) / count) * count
if start < 0:
start = 0
res = (
cursor.sort(
[
("field_label", ASC),
("conductor_norm", ASC),
("conductor_label", ASC),
("iso_label", ASC),
("number", ASC),
]
)
.skip(start)
.limit(count)
)
res = list(res)
for e in res:
e["numb"] = str(e["number"])
e["field_knowl"] = nf_display_knowl(e["field_label"], getDBConnection(), e["field_label"])
info["curves"] = res # [ECNF(e) for e in res]
info["number"] = nres
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
info["field_pretty"] = field_pretty
info["web_ainvs"] = web_ainvs
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
else:
info["report"] = "displaying all %s matches" % nres
t = "Elliptic Curve search results"
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
