def magma_output_iter(infilename): r""" Read Magma search output, as an iterator yielding the curves found. INPUT: - ``infilename`` (string) -- name of file containing Magma output """ infile = file(infilename) while True: try: L = infile.next() except StopIteration: raise StopIteration if 'Field' in L: field_label = L.split()[1] K = HilbertNumberField(field_label) KK = K.K() if 'Isogeny class' in L: class_label = L.split()[2] cond_label, iso_label = class_label.split("-") num = 0 if 'Conductor' in L: cond_ideal = L.replace("Conductor ", "") if 'Curve' in L: ai = [KK(a.encode()) for a in L[7:-2].split(",")] num += 1 yield field_label, cond_label, iso_label, num, cond_ideal, ai infile.close()
def find_curves(field_label='2.2.5.1', min_norm=0, max_norm=None, label=None, outfilename=None, verbose=False, effort=500): r""" Go through all Hilbert Modular Forms with the given field label, assumed totally real, for level norms in the given range, test whether an elliptic curve exists with the same label; if not, find the curves using Magma; output these to a file. """ print("Checking forms over {}, norms from {} to {}".format( field_label, min_norm, max_norm)) if outfilename: print("Output of curves found to {}".format(outfilename)) else: print("No curve search or output, just checking") query = {} query['field_label'] = field_label if fields.find({'label': field_label}).count() == 0: if verbose: print("No HMF data for field %s" % field_label) return None query['dimension'] = 1 # only look at rational newforms if label: print("looking for {} only".format(label)) query['short_label'] = label # e.g. '91.1-a' else: query['level_norm'] = {'$gte': int(min_norm)} if max_norm: query['level_norm']['$lte'] = int(max_norm) cursor = forms.find(query) cursor.sort([('level_norm', pymongo.ASCENDING)]) labels = [f['label'] for f in cursor] nfound = 0 nnotfound = 0 nok = 0 missing_curves = [] K = HilbertNumberField(field_label) primes = [P['ideal'] for P in K.primes_iter(1000)] curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap # Step 1: look at all newforms, check that there is an elliptic # curve of the same label, and if so compare ap-lists. The # dicts curve_ap and form_ap store these when there is # disagreement: e.g. curve_ap[conductor_label][iso_label] = # aplist. for curve_label in labels: # We find the forms again since otherwise the cursor might timeout during the loop. f = forms.find_one({'label': curve_label}) ec = nfcurves.find_one({ 'field_label': field_label, 'class_label': curve_label, 'number': 1 }) if ec: if verbose: print("curve with label %s found in the database" % curve_label) nfound += 1 ainvsK = parse_ainvs(K.K(), ec['ainvs']) E = EllipticCurve(ainvsK) good_flags = [E.has_good_reduction(P) for P in primes] good_primes = [P for (P, flag) in zip(primes, good_flags) if flag] aplist = [E.reduction(P).trace_of_frobenius() for P in good_primes] f_aplist = [int(a) for a in f['hecke_eigenvalues']] f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag] nap = min(len(aplist), len(f_aplist)) if aplist[:nap] == f_aplist[:nap]: nok += 1 if verbose: print("Curve {} and newform agree! (checked {} ap)".format( ec['short_label'], nap)) else: print("Curve {} does NOT agree with newform".format( ec['short_label'])) if verbose: for P, aPf, aPc in zip(good_primes[:nap], f_aplist[:nap], aplist[:nap]): if aPf != aPc: print("P = {} with norm {}".format( P, P.norm().factor())) print("ap from curve: %s" % aPc) print("ap from form: %s" % aPf) if not ec['conductor_label'] in curve_ap: curve_ap[ec['conductor_label']] = {} form_ap[ec['conductor_label']] = {} curve_ap[ec['conductor_label']][ec['iso_label']] = aplist form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist else: if verbose: print("No curve with label %s found in the database!" % curve_label) missing_curves.append(f['short_label']) nnotfound += 1 # Report progress: n = nfound + nnotfound if nnotfound: print( "Out of %s newforms, %s curves were found in the database and %s were not found" % (n, nfound, nnotfound)) else: print( "Out of %s newforms, all %s had curves with the same label and ap" % (n, nfound)) if nfound == nok: print("All curves agree with matching newforms") else: print("%s curves agree with matching newforms, %s do not" % (nok, nfound - nok)) if nnotfound: print("%s missing curves" % len(missing_curves)) else: return # Step 2: for each newform for which there was no curve, call interface to Magma's EllipticCurveSearch() # (unless outfilename is None in which case just dump the missing labels to a file) if outfilename: outfile = file(outfilename, mode="w") else: t = file("curves_missing.{}".format(field_label), mode="w") for c in missing_curves: t.write(c) t.write("\n") t.close() return def output(L): if outfilename: outfile.write(L) if verbose: sys.stdout.write(L) bad_p = [] #if field_label=='4.4.1600.1': bad_p = [7**2,13**2,29**2] if field_label == '4.4.2304.1': bad_p = [19**2, 29**2] if field_label == '4.4.4225.1': bad_p = [17**2, 23**2] if field_label == '4.4.7056.1': bad_p = [29**2, 31**2] if field_label == '4.4.7168.1': bad_p = [29**2] if field_label == '4.4.9248.1': bad_p = [23**2] if field_label == '4.4.11025.1': bad_p = [17**2, 37**2, 43**2] if field_label == '4.4.13824.1': bad_p = [19**2] if field_label == '4.4.12400.1': bad_p = [23**2] if field_label == '4.4.180769.1': bad_p = [23**2] if field_label == '6.6.905177.1': bad_p = [2**3] bad_p = [] effort0 = effort for nf_label in missing_curves: if verbose: print("Curve %s is missing from the database..." % nf_label) form = forms.find_one({ 'field_label': field_label, 'short_label': nf_label }) if not form: print("... form %s not found!" % nf_label) else: if verbose: print("... found form, calling Magma search") print("Conductor = %s" % form['level_ideal'].replace(" ", "")) N = K.ideal(form['level_label']) neigs = len(form['hecke_eigenvalues']) Plist = [P['ideal'] for P in K.primes_iter(neigs)] goodP = [(i, P) for i, P in enumerate(Plist) if not P.divides(N) and not P.norm() in bad_p and P.residue_class_degree() == 1] aplist = [int(form['hecke_eigenvalues'][i]) for i, P in goodP] Plist = [P for i, P in goodP] nap = len(Plist) neigs0 = min(nap, 100) effort = effort0 if verbose: print("Using %s ap from Hilbert newform and effort %s" % (neigs0, effort)) if bad_p: print("( excluding primes with norms {})".format(bad_p)) #inds = list(set([randint(0,nap-1) for _ in range(neigs0)])) inds = range(neigs0) Plist0 = [Plist[i] for i in inds] aplist0 = [aplist[i] for i in inds] curves = EllipticCurveSearch(K.K(), Plist0, N, aplist0, effort) # rep = 0 allrep = 0 while not curves and allrep < 10: allrep += 1 effort *= 2 # if rep<2: # rep += 1 # else: # rep = 1 # effort *=2 if verbose: print( "No curves found by Magma, trying again with effort %s..." % effort) curves = EllipticCurveSearch(K.K(), Plist0, N, aplist0, effort) if verbose: if curves: print("Success!") else: print("Still no success") E = None if curves: E = curves[0] print("%s curves for %s found, first is %s" % (len(curves), nf_label, E.ainvs())) else: print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") print("!!! No curves for %s found (using %s ap) !!!" % (nf_label, len(aplist))) print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") if E != None: ec = {} ec['field_label'] = field_label ec['conductor_label'] = form['level_label'] ec['iso_label'] = form['label_suffix'] ec['number'] = int(1) ec['conductor_ideal'] = form['level_ideal'].replace(" ", "") ec['conductor_norm'] = form['level_norm'] ai = E.ainvs() ec['ainvs'] = ";".join( [",".join([str(c) for c in list(a)]) for a in ai]) #print ec['ainvs'] ec['cm'] = '?' ec['base_change'] = [] output(make_curves_line(ec) + "\n") if outfilename: outfile.flush()
def check_curve_labels(field_label='2.2.5.1', min_norm=0, max_norm=None, fix=False, verbose=False): r""" Go through all curves with the given field label, assumed totally real, test whether a Hilbert Modular Form exists with the same label. """ query = {} query['field_label'] = field_label query['number'] = 1 # only look at first curve in each isogeny class query['conductor_norm'] = {'$gte': int(min_norm)} if max_norm: query['conductor_norm']['$lte'] = int(max_norm) else: max_norm = 'infinity' cursor = nfcurves.find(query) nfound = 0 nnotfound = 0 nok = 0 bad_curves = [] K = HilbertNumberField(field_label) primes = [P['ideal'] for P in K.primes_iter(30)] curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap # Step 1: look at all curves (one per isogeny class), check that # there is a Hilbert newform of the same label, and if so compare # ap-lists. The dicts curve_ap and form_ap store these when # there is disagreement: # e.g. curve_ap[conductor_label][iso_label] = aplist. for ec in cursor: hmf_label = "-".join( [ec['field_label'], ec['conductor_label'], ec['iso_label']]) f = forms.find_one({'field_label': field_label, 'label': hmf_label}) if f: if verbose: print("hmf with label %s found" % hmf_label) nfound += 1 ainvsK = parse_ainvs(K.K(), ec['ainvs']) E = EllipticCurve(ainvsK) good_flags = [E.has_good_reduction(P) for P in primes] good_primes = [P for (P, flag) in zip(primes, good_flags) if flag] aplist = [ E.reduction(P).trace_of_frobenius() for P in good_primes[:10] ] f_aplist = [int(a) for a in f['hecke_eigenvalues'][:30]] f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag][:10] if aplist == f_aplist: nok += 1 if verbose: print("Curve %s and newform agree!" % ec['short_label']) else: bad_curves.append(ec['short_label']) print("Curve %s does NOT agree with newform" % ec['short_label']) if verbose: print("ap from curve: %s" % aplist) print("ap from form: %s" % f_aplist) if not ec['conductor_label'] in curve_ap: curve_ap[ec['conductor_label']] = {} form_ap[ec['conductor_label']] = {} curve_ap[ec['conductor_label']][ec['iso_label']] = aplist form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist else: if verbose: print("No hmf with label %s found!" % hmf_label) nnotfound += 1 # Report progress: n = nfound + nnotfound if nnotfound: print("Out of %s forms, %s were found and %s were not found" % (n, nfound, nnotfound)) else: print( "Out of %s classes of curve, all %s had newforms with the same label" % (n, nfound)) if nfound == nok: print("All curves agree with matching newforms") else: print("%s curves agree with matching newforms, %s do not" % (nok, nfound - nok)) # print("Bad curves: %s" % bad_curves) # Step 2: for each conductor_label for which there was a # discrepancy, create a dict giving the permutation curve --> # newform, so remap[conductor_label][iso_label] = form_label remap = {} for level in curve_ap.keys(): remap[level] = {} c_dat = curve_ap[level] f_dat = form_ap[level] for a in c_dat.keys(): aplist = c_dat[a] for b in f_dat.keys(): if aplist == f_dat[b]: remap[level][a] = b break if verbose: print("remap: %s" % remap) # Step 3, for through all curves with these bad conductors and # create new labels for them, update the database with these (if # fix==True) for level in remap.keys(): perm = remap[level] print("Fixing iso labels for conductor %s using map %s" % (level, perm)) query = {} query['field_label'] = field_label query['conductor_label'] = level cursor = nfcurves.find(query) for ec in cursor: iso = ec['iso_label'] if iso in perm: new_iso = perm[iso] if verbose: print("--mapping class %s to class %s" % (iso, new_iso)) num = str(ec['number']) newlabeldata = {} newlabeldata['iso_label'] = new_iso newlabeldata['short_class_label'] = '-'.join([level, new_iso]) newlabeldata['class_label'] = '-'.join( [field_label, newlabeldata['short_class_label']]) newlabeldata['short_label'] = ''.join( [newlabeldata['short_class_label'], num]) newlabeldata['label'] = '-'.join( [field_label, newlabeldata['short_label']]) if verbose: print("new data fields: %s" % newlabeldata) if fix: nfcurves.update({'_id': ec['_id']}, {"$set": newlabeldata}, upsert=True)
def find_curve_labels(field_label='2.2.5.1', min_norm=0, max_norm=None, outfilename=None, verbose=False, effort=1000): r""" Go through all Hilbert Modular Forms with the given field label, assumed totally real, for level norms in the given range, test whether an elliptic curve exists with the same label. """ query = {} query['field_label'] = field_label if fields.find({'label': field_label}).count() == 0: if verbose: print("No HMF data for field %s" % field_label) return None query['dimension'] = 1 # only look at rational newforms query['level_norm'] = {'$gte': int(min_norm)} if max_norm: query['level_norm']['$lte'] = int(max_norm) else: max_norm = 'infinity' cursor = forms.find(query) cursor.sort([('level_norm', pymongo.ASCENDING)]) labels = [f['label'] for f in cursor] nfound = 0 nnotfound = 0 nok = 0 missing_curves = [] K = HilbertNumberField(field_label) primes = [P['ideal'] for P in K.primes_iter()] curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap # Step 1: look at all newforms, check that there is an elliptic # curve of the same label, and if so compare ap-lists. The # dicts curve_ap and form_ap store these when there is # disagreement: e.g. curve_ap[conductor_label][iso_label] = # aplist. for curve_label in labels: # We find the forms again since otherwise the cursor might timeout during the loop. f = forms.find_one({'label': curve_label}) ec = nfcurves.find_one({ 'field_label': field_label, 'class_label': curve_label, 'number': 1 }) if ec: if verbose: print("curve with label %s found" % curve_label) nfound += 1 ainvsK = parse_ainvs(K.K(), ec['ainvs']) E = EllipticCurve(ainvsK) good_flags = [E.has_good_reduction(P) for P in primes] good_primes = [P for (P, flag) in zip(primes, good_flags) if flag] aplist = [ E.reduction(P).trace_of_frobenius() for P in good_primes[:30] ] f_aplist = [int(a) for a in f['hecke_eigenvalues'][:40]] f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag][:30] if aplist == f_aplist: nok += 1 if verbose: print("Curve %s and newform agree!" % ec['short_label']) else: print("Curve %s does NOT agree with newform" % ec['short_label']) if verbose: print("ap from curve: %s" % aplist) print("ap from form: %s" % f_aplist) if not ec['conductor_label'] in curve_ap: curve_ap[ec['conductor_label']] = {} form_ap[ec['conductor_label']] = {} curve_ap[ec['conductor_label']][ec['iso_label']] = aplist form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist else: if verbose: print("No curve with label %s found!" % curve_label) missing_curves.append(f['short_label']) nnotfound += 1 # Report progress: n = nfound + nnotfound if nnotfound: print( "Out of %s newforms, %s curves were found and %s were not found" % (n, nfound, nnotfound)) else: print( "Out of %s newforms, all %s had curves with the same label and ap" % (n, nfound)) if nfound == nok: print("All curves agree with matching newforms") else: print("%s curves agree with matching newforms, %s do not" % (nok, nfound - nok)) if nnotfound: print("Missing curves: %s" % missing_curves) else: return if outfilename == None: return # Step 2: for each newform for which there was no curve, create a # Magma file containing code to search for such a curve. # First output Magma code to define the field and primes: output_magma_field(field_label, K.K(), primes, outfilename) if verbose: print("...output definition of field and primes finished") for nf_label in missing_curves: if verbose: print("Curve %s is missing..." % nf_label) form = forms.find_one({ 'field_label': field_label, 'short_label': nf_label }) if not form: print("... form %s not found!" % nf_label) else: if verbose: print("... found form, outputting Magma search code") output_magma_curve_search(K, form, outfilename, verbose=verbose, effort=effort)
def find_curves(field_label='2.2.5.1', min_norm=0, max_norm=None, outfilename=None, verbose=False): r""" Go through all Hilbert Modular Forms with the given field label, assumed totally real, for level norms in the given range, test whether an elliptic curve exists with the same label; if not, find the curves using Magma; output these to a file. """ query = {} query['field_label'] = field_label if fields.find({'label': field_label}).count() == 0: if verbose: print("No HMF data for field %s" % field_label) return None query['dimension'] = 1 # only look at rational newforms query['level_norm'] = {'$gte': int(min_norm)} if max_norm: query['level_norm']['$lte'] = int(max_norm) else: max_norm = 'infinity' cursor = forms.find(query) nfound = 0 nnotfound = 0 nok = 0 missing_curves = [] K = HilbertNumberField(field_label) primes = [P['ideal'] for P in K.primes_iter(100)] curve_ap = {} # curve_ap[conductor_label] will be a dict iso -> ap form_ap = {} # form_ap[conductor_label] will be a dict iso -> ap # Step 1: look at all newforms, check that there is an elliptic # curve of the same label, and if so compare ap-lists. The # dicts curve_ap and form_ap store these when there is # disagreement: e.g. curve_ap[conductor_label][iso_label] = # aplist. for f in cursor: curve_label = f['label'] ec = nfcurves.find_one({ 'field_label': field_label, 'class_label': curve_label, 'number': 1 }) if ec: if verbose: print("curve with label %s found in the database" % curve_label) nfound += 1 ainvsK = [K.K()([QQ(str(c)) for c in ai]) for ai in ec['ainvs']] E = EllipticCurve(ainvsK) good_flags = [E.has_good_reduction(P) for P in primes] good_primes = [P for (P, flag) in zip(primes, good_flags) if flag] aplist = [ E.reduction(P).trace_of_frobenius() for P in good_primes[:30] ] f_aplist = [int(a) for a in f['hecke_eigenvalues'][:40]] f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag][:30] if aplist == f_aplist: nok += 1 if verbose: print("Curve %s and newform agree!" % ec['short_label']) else: print("Curve %s does NOT agree with newform" % ec['short_label']) if verbose: print("ap from curve: %s" % aplist) print("ap from form: %s" % f_aplist) if not ec['conductor_label'] in curve_ap: curve_ap[ec['conductor_label']] = {} form_ap[ec['conductor_label']] = {} curve_ap[ec['conductor_label']][ec['iso_label']] = aplist form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist else: if verbose: print("No curve with label %s found in the database!" % curve_label) missing_curves.append(f['short_label']) nnotfound += 1 # Report progress: n = nfound + nnotfound if nnotfound: print( "Out of %s newforms, %s curves were found in the database and %s were not found" % (n, nfound, nnotfound)) else: print( "Out of %s newforms, all %s had curves with the same label and ap" % (n, nfound)) if nfound == nok: print("All curves agree with matching newforms") else: print("%s curves agree with matching newforms, %s do not" % (nok, nfound - nok)) if nnotfound: print("Missing curves: %s" % missing_curves) else: return # Step 2: for each newform for which there was no curve, call interface to Magma's EllipticCurveSearch() if outfilename: outfile = file(outfilename, mode="w") def output(L): if outfilename: outfile.write(L) if verbose: sys.stdout.write(L) for nf_label in missing_curves: if verbose: print("Curve %s is missing from the database..." % nf_label) form = forms.find_one({ 'field_label': field_label, 'short_label': nf_label }) if not form: print("... form %s not found!" % nf_label) else: if verbose: print("... found form, calling Magma search") N = K.ideal(form['level_label']) Plist = [P['ideal'] for P in K.primes_iter(30)] goodP = [(i, P) for i, P in enumerate(Plist) if not P.divides(N)] label = form['short_label'] aplist = [int(form['hecke_eigenvalues'][i]) for i, P in goodP] curves = EllipticCurveSearch(K.K(), Plist, N, aplist[:5]) #curves = EllipticCurveSearch(K.K(), [], N, []) if curves: E = curves[0] print("%s curves found by Magma, first is %s" % (len(curves), E)) else: print("No curves found by Magma (using %s ap)" % len(aplist)) ec = {} ec['field_label'] = field_label ec['conductor_label'] = form['level_label'] ec['iso_label'] = form['label_suffix'] ec['number'] = int(1) ec['conductor_ideal'] = form['level_ideal'].replace(" ", "") ec['conductor_norm'] = form['level_norm'] ai = E.ainvs() ec['ainvs'] = [[str(c) for c in list(a)] for a in ai] ec['cm'] = '?' ec['base_change'] = [] output(make_curves_line(ec) + "\n")