def make_extra_data(label, number, ainvs, gens): """Given a curve label (and number, as some data is only stored wih curve number 1 in each class) and its ainvs and gens, returns a dict with which to update the entry. Extra items computed here: 'equation': latex string of curve's equation 'signD': sign of discriminant 'local_data': list of dicts, one item for each bad prime 'min_quad_twist': dict holding curve's min quadratic twist and the twisting discriminant 'heights': list of heights of gens and for curve #1 in a class only: 'aplist': list of a_p for p<100 'anlist': list of a_n for n<=20 """ E = EllipticCurve(parse_ainvs(ainvs)) data = {} # convert from a list of strings to a single string, e.g. from ['0','0','0','1','1'] to '[0,0,0,1,1]' data['equation'] = web_latex(E) data['signD'] = int(E.discriminant().sign()) data['local_data'] = [{ 'p': int(ld.prime().gen()), 'ord_cond': int(ld.conductor_valuation()), 'ord_disc': int(ld.discriminant_valuation()), 'ord_den_j': int(max(0, -(E.j_invariant().valuation(ld.prime().gen())))), 'red': int(ld.bad_reduction_type()), 'rootno': int(E.root_number(ld.prime().gen())), 'kod': web_latex(ld.kodaira_symbol()).replace('$', ''), 'cp': int(ld.tamagawa_number()) } for ld in E.local_data()] Etw, Dtw = E.minimal_quadratic_twist() if Etw.conductor() == E.conductor(): data['min_quad_twist'] = {'label': label, 'disc': int(1)} else: minq_ainvs = ''.join(['['] + [str(c) for c in Etw.ainvs()] + [']']) r = curves.find_one({ 'jinv': str(E.j_invariant()), 'ainvs': minq_ainvs }) minq_label = "" if r is None else r['label'] data['min_quad_twist'] = {'label': minq_label, 'disc': int(Dtw)} from lmfdb.elliptic_curves.web_ec import parse_points gens = [E(g) for g in parse_points(gens)] data['heights'] = [float(P.height()) for P in gens] if number == 1: data['aplist'] = E.aplist(100, python_ints=True) data['anlist'] = E.anlist(20, python_ints=True) return data
def make_extra_data(label, number, ainvs, gens): """ C is a database elliptic curve entry. Returns a dict with which to update the entry. Data fields needed in C already: 'ainvs', 'lmfdb_label', 'gens', 'number' """ E = EllipticCurve([int(a) for a in ainvs]) data = {} # convert from a list of strings to a single string, e.g. from ['0','0','0','1','1'] to '[0,0,0,1,1]' data['xainvs'] = ''.join(['[', ','.join(ainvs), ']']) data['equation'] = web_latex(E) data['signD'] = int(E.discriminant().sign()) data['local_data'] = [{ 'p': int(ld.prime().gen()), 'ord_cond': int(ld.conductor_valuation()), 'ord_disc': int(ld.discriminant_valuation()), 'ord_den_j': int(max(0, -(E.j_invariant().valuation(ld.prime().gen())))), 'red': int(ld.bad_reduction_type()), 'rootno': int(E.root_number(ld.prime().gen())), 'kod': web_latex(ld.kodaira_symbol()).replace('$', ''), 'cp': int(ld.tamagawa_number()) } for ld in E.local_data()] Etw, Dtw = E.minimal_quadratic_twist() if Etw.conductor() == E.conductor(): data['min_quad_twist'] = {'label': label, 'disc': int(1)} else: # Later this should be changed to look for xainvs but now all curves have ainvs minq_ainvs = [str(c) for c in Etw.ainvs()] r = curves.find_one({ 'jinv': str(E.j_invariant()), 'ainvs': minq_ainvs }) minq_label = "" if r is None else r['label'] data['min_quad_twist'] = {'label': minq_label, 'disc': int(Dtw)} from lmfdb.elliptic_curves.web_ec import parse_points gens = [E(g) for g in parse_points(gens)] data['heights'] = [float(P.height()) for P in gens] if number == 1: data['aplist'] = E.aplist(100, python_ints=True) data['anlist'] = E.anlist(20, python_ints=True) return data
def make_extra_data(label,number,ainvs,gens): """Given a curve label (and number, as some data is only stored wih curve number 1 in each class) and its ainvs and gens, returns a dict with which to update the entry. Extra items computed here: 'equation': latex string of curve's equation 'signD': sign of discriminant 'local_data': list of dicts, one item for each bad prime 'min_quad_twist': dict holding curve's min quadratic twist and the twisting discriminant 'heights': list of heights of gens and for curve #1 in a class only: 'aplist': list of a_p for p<100 'anlist': list of a_n for n<=20 """ E = EllipticCurve(parse_ainvs(ainvs)) data = {} # convert from a list of strings to a single string, e.g. from ['0','0','0','1','1'] to '[0,0,0,1,1]' data['equation'] = web_latex(E) data['signD'] = int(E.discriminant().sign()) data['local_data'] = [{'p': int(ld.prime().gen()), 'ord_cond':int(ld.conductor_valuation()), 'ord_disc':int(ld.discriminant_valuation()), 'ord_den_j':int(max(0,-(E.j_invariant().valuation(ld.prime().gen())))), 'red':int(ld.bad_reduction_type()), 'rootno':int(E.root_number(ld.prime().gen())), 'kod':web_latex(ld.kodaira_symbol()).replace('$',''), 'cp':int(ld.tamagawa_number())} for ld in E.local_data()] Etw, Dtw = E.minimal_quadratic_twist() if Etw.conductor()==E.conductor(): data['min_quad_twist'] = {'label':label, 'disc':int(1)} else: minq_ainvs = ''.join(['['] + [str(c) for c in Etw.ainvs()] + [']']) r = curves.find_one({'jinv':str(E.j_invariant()), 'ainvs':minq_ainvs}) minq_label = "" if r is None else r['label'] data['min_quad_twist'] = {'label':minq_label, 'disc':int(Dtw)} from lmfdb.elliptic_curves.web_ec import parse_points gens = [E(g) for g in parse_points(gens)] data['heights'] = [float(P.height()) for P in gens] if number==1: data['aplist'] = E.aplist(100,python_ints=True) data['anlist'] = E.anlist(20,python_ints=True) return data
def download_EC_all(label): CDB = lmfdb.base.getDBConnection().elliptic_curves.curves N, iso, number = split_lmfdb_label(label) if number: data = CDB.find_one({'lmfdb_label': label}) if data is None: return elliptic_curve_jump_error(label, {}) data_list = [data] else: data_list = sorted(list(CDB.find({'lmfdb_iso': label})), key=lambda E: E['number']) if len(data_list) == 0: return elliptic_curve_jump_error(label, {}) # titles of all entries of curves dump_data = [] titles = [str(c) for c in data_list[0]] titles = [t for t in titles if t[0] != '_'] titles.sort() dump_data.append(titles) for data in data_list: data1 = [] for t in titles: d = data[t] if t == 'ainvs': data1.append(format_ainvs(d)) elif t in ['torsion_generators', 'torsion_structure']: data1.append([eval(g) for g in d]) elif t == 'x-coordinates_of_integral_points': data1.append(parse_list(d)) elif t == 'gens': data1.append(parse_points(d)) elif t in ['iso', 'label', 'lmfdb_iso', 'lmfdb_label']: data1.append(str(d)) else: data1.append(d) dump_data.append(data1) response = make_response('\n'.join(str(an) for an in dump_data)) response.headers['Content-type'] = 'text/plain' return response
def download_EC_all(label): CDB = lmfdb.base.getDBConnection().elliptic_curves.curves N, iso, number = split_lmfdb_label(label) if number: data = CDB.find_one({"lmfdb_label": label}) if data is None: return elliptic_curve_jump_error(label, {}) data_list = [data] else: data_list = sorted(list(CDB.find({"lmfdb_iso": label})), key=lambda E: E["number"]) if len(data_list) == 0: return elliptic_curve_jump_error(label, {}) # titles of all entries of curves dump_data = [] titles = [str(c) for c in data_list[0]] titles = [t for t in titles if t[0] != "_"] titles.sort() dump_data.append(titles) for data in data_list: data1 = [] for t in titles: d = data[t] if t == "ainvs": data1.append(format_ainvs(d)) elif t in ["torsion_generators", "torsion_structure"]: data1.append([eval(g) for g in d]) elif t == "x-coordinates_of_integral_points": data1.append(split_list(d)) elif t == "gens": data1.append(parse_points(d)) elif t in ["iso", "label", "lmfdb_iso", "lmfdb_label"]: data1.append(str(d)) else: data1.append(d) dump_data.append(data1) response = make_response("\n".join(str(an) for an in dump_data)) response.headers["Content-type"] = "text/plain" return response
def make_extra_data(label,number,ainvs,gens): """ C is a database elliptic curve entry. Returns a dict with which to update the entry. Data fields needed in C already: 'ainvs', 'lmfdb_label', 'gens', 'number' """ E = EllipticCurve([int(a) for a in ainvs]) data = {} # convert from a list of strings to a single string, e.g. from ['0','0','0','1','1'] to '[0,0,0,1,1]' data['xainvs'] = ''.join(['[',','.join(ainvs),']']) data['equation'] = web_latex(E) data['signD'] = int(E.discriminant().sign()) data['local_data'] = [{'p': int(ld.prime().gen()), 'ord_cond':int(ld.conductor_valuation()), 'ord_disc':int(ld.discriminant_valuation()), 'ord_den_j':int(max(0,-(E.j_invariant().valuation(ld.prime().gen())))), 'red':int(ld.bad_reduction_type()), 'rootno':int(E.root_number(ld.prime().gen())), 'kod':web_latex(ld.kodaira_symbol()).replace('$',''), 'cp':int(ld.tamagawa_number())} for ld in E.local_data()] Etw, Dtw = E.minimal_quadratic_twist() if Etw.conductor()==E.conductor(): data['min_quad_twist'] = {'label':label, 'disc':int(1)} else: # Later this should be changed to look for xainvs but now all curves have ainvs minq_ainvs = [str(c) for c in Etw.ainvs()] r = curves.find_one({'jinv':str(E.j_invariant()), 'ainvs':minq_ainvs}) minq_label = "" if r is None else r['label'] data['min_quad_twist'] = {'label':minq_label, 'disc':int(Dtw)} from lmfdb.elliptic_curves.web_ec import parse_points gens = [E(g) for g in parse_points(gens)] data['heights'] = [float(P.height()) for P in gens] if number==1: data['aplist'] = E.aplist(100,python_ints=True) data['anlist'] = E.anlist(20,python_ints=True) return data
def allgens(line): r""" Parses one line from an allgens file. Returns the label and a dict containing fields with keys 'conductor', 'iso', 'number', 'ainvs', 'jinv', 'cm', 'rank', 'gens', 'torsion_order', 'torsion_structure', 'torsion_generators', all values being strings or ints, and more. Input line fields: conductor iso number ainvs rank torsion_structure gens torsion_gens Sample input line: 20202 i 2 [1,0,0,-298389,54947169] 1 [2,4] [-570:6603:1] [-622:311:1] [834:19239:1] """ global lmfdb_label_to_label global label_to_lmfdb_label data = split(line) iso = data[0] + data[1] label = iso + data[2] try: lmfdb_label = label_to_lmfdb_label[label] except AttributeError: print("Label {} not found in label_to_lmfdb_label dict!".format(label)) lmfdb_label = "" global nallgens nallgens += 1 if nallgens % 100 == 0: print("processing allgens for {} (#{})".format(label, nallgens)) rank = int(data[4]) t = data[5] tor_struct = [] if t == '[]' else t[1:-1].split(",") torsion = int(prod([int(ti) for ti in tor_struct], 1)) ainvs = parse_ainvs(data[3]) E = EllipticCurve(ainvs) jinv = text_type(E.j_invariant()) if E.has_cm(): cm = int(E.cm_discriminant()) else: cm = int(0) N = E.conductor() bad_p = N.prime_factors() # will be sorted num_bad_p = len(bad_p) local_data = [{ 'p': int(ld.prime().gen()), 'ord_cond': int(ld.conductor_valuation()), 'ord_disc': int(ld.discriminant_valuation()), 'ord_den_j': int(max(0, -(E.j_invariant().valuation(ld.prime().gen())))), 'red': int(ld.bad_reduction_type()), 'rootno': int(E.root_number(ld.prime().gen())), 'kod': web_latex(ld.kodaira_symbol()).replace('$', ''), 'cp': int(ld.tamagawa_number()) } for ld in E.local_data()] semistable = all([ld['ord_cond'] == 1 for ld in local_data]) gens = [ gen.replace("[", "(").replace("]", ")") for gen in data[6:6 + rank] ] tor_gens = ["%s" % parse_tgens(tgens[1:-1]) for tgens in data[6 + rank:]] from lmfdb.elliptic_curves.web_ec import parse_points heights = [float(E(P).height()) for P in parse_points(gens)] Etw, Dtw = E.minimal_quadratic_twist() if Etw.conductor() == N: min_quad_twist = { 'label': label, 'lmfdb_label': lmfdb_label, 'disc': int(1) } else: minq_ainvs = Etw.ainvs() r = curves.lucky({ 'jinv': str(E.j_invariant()), 'ainvs': minq_ainvs }, projection=['label', 'lmfdb_label']) min_quad_twist = { 'label': r['label'], 'lmfdb_label': r['lmfdb_label'], 'disc': int(Dtw) } trace_hash = TraceHashClass(iso, E) return label, { 'conductor': int(data[0]), 'iso': iso, 'number': int(data[2]), 'ainvs': ainvs, 'jinv': jinv, 'cm': cm, 'rank': rank, 'gens': gens, 'torsion': torsion, 'torsion_structure': tor_struct, 'torsion_generators': tor_gens, 'trace_hash': trace_hash, 'equation': web_latex(E), 'bad_primes': bad_p, 'num_bad_primes': num_bad_p, 'local_data': local_data, 'semistable': semistable, 'signD': int(E.discriminant().sign()), 'heights': heights, 'aplist': E.aplist(100, python_ints=True), 'anlist': E.anlist(20, python_ints=True), 'min_quad_twist': min_quad_twist, }