-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': 0, 'Lhash': '683396174768019189', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 298.9599051676739, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '37440.1', 'coefficient_field': '1.1.1.1', 'conductor': 37440, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, -3, 7], [1, -3, 11], [1, 1], [1, 3, 17], [1, -4, 19], [1, -3, 23], [1, -10, 29], [1, -6, 31], [1, -5, 37], [1, -5, 41], [1, -2, 43], [1, 2, 47], [1, -11, 53], [1, -4, 59], [1, 1, 61], [1, 4, 67], [1, 3, 71], [1, -6, 73], [1, 3, 79], [1, -16, 83], [1, -7, 89], [1, 19, 97]], 'gamma_factors': [[], [0]], 'index': 63, 'label': '2-37440-1.1-c1-0-63', 'leading_term': '3.36820253995', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/37440/cn', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.368202539948972, 2.900124338731996, 1.659935746932757, 0.228807249120704, -0.4752482745884306, 0.1777533363215667, 1.770640360796564, 2.867313074648637, 2.203945190574623, 0.1093058627476997, -1.46685047051103, -0.804037465022761, 1.573372449658908, 3.142426115090048, 2.064242941808593, -0.6128552805831213, -2.086268446891541, -1.199497144106783, 0.1611811755263703, -0.2529132220051151, -1.716094153301431, -1.343659496885348, 1.630611250385708, 4.12237751846179, 3.049692008797685, -0.2488615207029034, -1.577239414007374, 0.3380210050954562, 2.154781644406171, 0.9857346844587503, -1.306771935349777, -1.206923588230386, 0.8127951398869604, 1.179920335388534, -0.7142047615700369, -1.38013235141388, 0.7150019599841204, 1.998353099472494, -0.5084711461703337, -3.701246511528503, -2.803009114080805, 0.9190343655265518, 1.962759701655404, -0.7210952259295537, -2.499964397884097, -1.046677124878282, 0.3842549607926367, -0.3716943784403541, -0.4296043493026757, 1.933735089591623, 2.769460877320871, -0.8402947384117633, -4.451165199679731, -2.764109291023522, 1.521097872331015, 2.277654872070895, 0.09633621976590077, 0.1155100192006549, 2.220751258632671, 1.977401198137349, -0.1714127138435513, 0.293556417615263, 2.63807985409942, 1.737062430897325, -1.775840173385182, -1.980556318630918, 1.216901813751172, 1.593354923500819, -1.804008825231385, -3.062705547059467, -0.6749469764141608, 0.4372099544209738, -0.4319201230314527, 1.539106674773097, 5.774543660118961, 5.822061274892874, 1.484587354756032, -0.4235244078732012, 1.326243880033123, 1.216614874869818, -1.057444488232876, -0.2691772157042155, 2.730956259276701, 2.192671087122713, -0.6058923415087402, 0.1856347513008562, 2.768880950977929, 1.369992039097105, -1.471065592310392, 0.08392104489158617, 2.921702921257119, 1.273214445316316, -1.365018806629564, 0.2878108607251746, 2.168547562708092, -0.4579379533097459, -3.054683500971211, -1.437181760902409, 0.1592265944686751, -0.6107736245768465, 0.6613639182099434, 3.317895361442693, 0.5429109448033415, -5.7965925681086, -6.188361017712453, -0.9114172398796504, 1.071601658948145, -0.8874716784464322, -0.6810581182068312, 0.7710826342334548, -0.2456805844484869, -0.2597263189050062, 2.892484897986379, 3.148969183043517, -1.055884682626273, -2.251953317903737, 0.3763674640015322, -1.044341789277765, -5.735937122822818, -4.997972419584827, -0.01936854226553118], 'positive_zeros': ['0.7999837175867387', '1.213568556601413', '2.262360014926309', '2.843829479972202', '3.692176749919461', '4.452780188213476', '4.697495752223130', '5.379539239721063', '6.229547761202106', '6.717673595392525', '7.347067716367268', '7.899600082948979', '8.414961384881553', '8.930630737380632', '9.466006799825704', '10.18501545754530', '10.69355861616082', '11.38628419757407', '11.66920700545516', '12.06166559671977', '12.70608901824452', '13.40242219557712', '14.01448864094597', '14.23246593272111', '14.97290514236963', '15.21354158716267', '15.87064314606252', '16.40606003248421', '16.87774840000949', '17.57546185869421', '17.86644955564670', '18.12500058831115', '19.11263060913237', '19.33435476269423', '19.87632592031322'], 'prelabel': '2-37440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.290457054909623, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 683396174768019189, 'z1': {'__RealLiteral__': 0, 'data': '0.7999837175867387', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.213568556601413', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.262360014926309', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 298.9599051676739, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 37440, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 3, 0, -1, 0, 0, 0, -3, 0, 4, 0, 0, 0, 3, 0, 1, 0, 0, 0, 10, 0, 6, 0, 0, 0, -3, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 11, 0, -3, 0, 0, 0, 4, 0, -1, 0, 0, 0, 1, 0, -4, 0, 0, 0, -3, 0, 6, 0, 0, 0, 9, 0, -3, 0, 0, 0, 16, 0, 3, 0, 0, 0, 7, 0, -3, 0, 0, 0, -4, 0, -19, 0, 0, 0], 'euler11': [1, -3, 11], 'euler13': [1, 1, 0], 'euler17': [1, 3, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, -6, 31], 'euler37': [1, -5, 37], 'euler41': [1, -5, 41], 'euler43': [1, -2, 43], 'euler47': [1, 2, 47], 'euler5': [1, 1, 0], 'euler53': [1, -11, 53], 'euler59': [1, -4, 59], 'euler61': [1, 1, 61], 'euler67': [1, 4, 67], 'euler7': [1, -3, 7], 'euler71': [1, 3, 71], 'euler73': [1, -6, 73], 'euler79': [1, 3, 79], 'euler83': [1, -16, 83], 'euler89': [1, -7, 89], 'euler97': [1, 19, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -3, 7], [1, -3, 11], [1, 1, 0], [1, 3, 17], [1, -4, 19], [1, -3, 23], [1, -10, 29], [1, -6, 31], [1, -5, 37], [1, -5, 41], [1, -2, 43], [1, 2, 47], [1, -11, 53], [1, -4, 59], [1, 1, 61], [1, 4, 67], [1, 3, 71], [1, -6, 73], [1, 3, 79], [1, -16, 83], [1, -7, 89], [1, 19, 97]], 'index': 63, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/37440/cn'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-37440-1.1-c1-0-63', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-37440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.290457054909623, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 683396174768019189, 'z1': {'__RealLiteral__': 0, 'data': '0.7999837175867387', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '683396174768019189', 'Lhash_array': ['683396174768019189'], 'label': '2-37440-1.1-c1-0-63', 'type': 'ECQ', 'url': 'EllipticCurve/Q/37440/cn'}