Elliptic curve data - 45570.cr5

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '45570da', 'Clabel': '45570da1', 'Cnumber': 1, 'abc_quality': 0.9769413028263426, 'absD': 272482901747814240000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 3472, 'ainvs': [1, 0, 0, 974609, -702485575], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 45570, 'degree': 1966080, 'elladic_images': ['16.48.0.106'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6048325820721440933981224410', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 69, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [870215264126076959, 2316066449760000], 'lmfdb_iso': '45570.cr', 'lmfdb_label': '45570.cr5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 19890, 2056587], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '16.48.0-8.bb.1.4', '28.12.0-4.c.1.2', '56.48.0-8.bb.1.7', '62.6.0.b.1', '112.96.0.?', '124.12.0.?', '248.48.0.?', '496.96.0.?', '868.24.0.?', '1736.96.0.?', '3472.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.8211608041026632118677122222', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1519], [3, 4, 15190], [5, 6, 9114], [7, 32, 930], [31, 32, 1470]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6318775075444874408454460693', 'prec': 100}, 'szpiro_ratio': 5.058601929312919, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 1, 1, 1, -1, 1, 0, 1, 1, -1, -4, 1, 2, 0, -1, 1, 6, 1, -4, -1], 'aplist': [1, 1, -1, 0, -4, 2, 6, -4, 0, 6, 1, -2, -10, -4, 0, -2, -12, -14, 4, 8, -2, 8, -12, -2, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 45570, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '45570.cr', 'trace_hash': 618572189323423464}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.0054635027580256830728302454751', 'prec': 110}, 'conductor': 45570, 'gens': [[578, 7061, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8211608041026632118677122222', 'prec': 100}], 'lmfdb_label': '45570.cr5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.089592162878772267397617585881', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.442351064934507278467725429755944905', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[550, -275, 1]], 'xcoord_integral_points': [550, 578, 16934, 67778]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [12, 0], '3': [2, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [2, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '45570.cr5'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 2225820
    {'degree': 2, 'field': [-54, -1, 1], 'lmfdb_label': '45570.cr5', 'torsion': [4]}
  • id: 2225821
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '45570.cr5', 'torsion': [8]}
  • id: 2225819
    {'degree': 2, 'field': [8, -1, 1], 'lmfdb_label': '45570.cr5', 'torsion': [2, 2]}
  • id: 2225822
    {'degree': 4, 'field': [36, 0, 19, 0, 1], 'lmfdb_label': '45570.cr5', 'torsion': [2, 8]}
  • id: 2225826
    {'degree': 8, 'field': [-13592, 500, -98, -805, 406, -7, 7, -4, 1], 'lmfdb_label': '45570.cr5', 'torsion': [6]}
  • id: 2225824
    {'degree': 8, 'field': [-24, 184, -186, 10, -19, 14, 0, -4, 1], 'lmfdb_label': '45570.cr5', 'torsion': [8]}
  • id: 2225825
    {'degree': 8, 'field': [2776, 728, -634, -216, 179, -88, 34, -4, 1], 'lmfdb_label': '45570.cr5', 'torsion': [16]}
  • id: 2225823
    {'degree': 8, 'field': [6400, 0, 1232, 0, 356, 0, -28, 0, 1], 'lmfdb_label': '45570.cr5', 'torsion': [2, 4]}
  • id: 2225827
    {'degree': 16, 'field': [576, 0, 24928, 0, 31828, 0, -1816, 0, 1505, 0, 488, 0, 74, 0, 16, 0, 1], 'lmfdb_label': '45570.cr5', 'torsion': [4, 8]}
  • id: 2225833
    {'degree': 16, 'field': [14889728, 5075840, 19501120, -9067712, 2748992, -106512, -358160, -117224, 68396, -7484, -996, 1177, 44, -21, 11, -4, 1], 'lmfdb_label': '45570.cr5', 'torsion': [24]}
  • id: 2225829
    {'degree': 16, 'field': [58169344, -54624256, 3485952, 3980672, 1701592, 239944, 153350, 64920, 80671, -9792, -2446, 1044, 368, -48, 32, -4, 1], 'lmfdb_label': '45570.cr5', 'torsion': [2, 16]}
  • id: 2225830
    {'degree': 16, 'field': [263481408, -608618304, 563404896, -257430480, 60338692, -10374064, 2337472, 335044, -328055, 28208, -15544, 5552, 274, -32, -8, -4, 1], 'lmfdb_label': '45570.cr5', 'torsion': [16]}
  • id: 2225831
    {'degree': 16, 'field': [388878400, 0, 1115846864, 0, -121898420, 0, 2546327, 0, -291998, 0, 12215, 0, 2485, 0, 62, 0, 1], 'lmfdb_label': '45570.cr5', 'torsion': [2, 6]}
  • id: 2225832
    {'degree': 16, 'field': [181639620864, 0, 68477901612, 0, 348449824, 0, -669383664, 0, 17246469, 0, 94768, 0, -8706, 0, 0, 0, 1], 'lmfdb_label': '45570.cr5', 'torsion': [12]}
  • id: 2225828
    {'degree': 16, 'field': [793841033216, 240102567936, -109889302528, -35874992256, 7075887624, 2448578904, -308824990, -105140760, 10127323, 3003080, -269330, -57196, 5924, 744, -88, -4, 1], 'lmfdb_label': '45570.cr5', 'torsion': [2, 16]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 1085731
    {'conductor': 45570, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '45570.cr5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1085732
    {'conductor': 45570, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '45570.cr5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1085733
    {'conductor': 45570, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '45570.cr5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1085734
    {'conductor': 45570, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '45570.cr5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1085735
    {'conductor': 45570, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '45570.cr5', 'prime': 31, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1967698
    {'adelic_gens': [[2032, 5, 2531, 3458], [1, 16, 868, 869], [1, 16, 0, 1], [5, 4, 3468, 3469], [1313, 16, 370, 2511], [1, 0, 16, 1], [3457, 16, 3456, 17], [991, 3456, 984, 3343], [15, 2, 3374, 3459]], 'adelic_image': '3472.192.1.?', 'conductor': 45570, 'lmfdb_label': '45570.cr5', 'prime': 0}
  • id: 197516
    {'conductor': 45570, 'elladic_image': '16.48.0.106', 'lmfdb_label': '45570.cr5', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 2280124
    {'lmfdb_iso': '45570.cr', 'p': 11, 'prec': 20, 'unit': 13868968747779856470, 'val': 1}
  • id: 2280122
    {'lmfdb_iso': '45570.cr', 'p': 13, 'prec': 20, 'unit': 1289658426878687688047, 'val': 1}
  • id: 2280125
    {'lmfdb_iso': '45570.cr', 'p': 17, 'prec': 20, 'unit': 126689021296021888516409, 'val': 1}
  • id: 2280126
    {'lmfdb_iso': '45570.cr', 'p': 19, 'prec': 20, 'unit': 1655565648855786353128051, 'val': 1}
  • id: 2280121
    {'lmfdb_iso': '45570.cr', 'p': 29, 'prec': 20, 'unit': 3594133623446450209339363070, 'val': 1}
  • id: 2280117
    {'lmfdb_iso': '45570.cr', 'p': 37, 'prec': 20, 'unit': 69951595857604130818970239863, 'val': 1}
  • id: 2280119
    {'lmfdb_iso': '45570.cr', 'p': 41, 'prec': 20, 'unit': 636127029779469211606085280478, 'val': 1}
  • id: 2280120
    {'lmfdb_iso': '45570.cr', 'p': 43, 'prec': 20, 'unit': 1430557130955081930243235049818, 'val': 1}
  • id: 2280127
    {'lmfdb_iso': '45570.cr', 'p': 53, 'prec': 20, 'unit': 284901809456333908657979829615238, 'val': 1}
  • id: 2280130
    {'lmfdb_iso': '45570.cr', 'p': 59, 'prec': 20, 'unit': 723986980999446717152327175249796, 'val': 1}
  • id: 2280131
    {'lmfdb_iso': '45570.cr', 'p': 61, 'prec': 20, 'unit': 1852540070184920407990633022030755, 'val': 1}
  • id: 2280116
    {'lmfdb_iso': '45570.cr', 'p': 67, 'prec': 20, 'unit': 27990515074286369145406563042311037, 'val': 1}
  • id: 2280118
    {'lmfdb_iso': '45570.cr', 'p': 71, 'prec': 20, 'unit': 125120436577780914787734947791270126, 'val': 1}
  • id: 2280128
    {'lmfdb_iso': '45570.cr', 'p': 73, 'prec': 20, 'unit': 122045789850136253899579958741833567, 'val': 1}
  • id: 2280123
    {'lmfdb_iso': '45570.cr', 'p': 79, 'prec': 20, 'unit': 662515738825064266098434356781658365, 'val': 1}
  • id: 2280115
    {'lmfdb_iso': '45570.cr', 'p': 83, 'prec': 20, 'unit': 2107855113430111986660189391066500473, 'val': 1}
  • id: 2280129
    {'lmfdb_iso': '45570.cr', 'p': 89, 'prec': 20, 'unit': 4600478778386227966779319593851583905, 'val': 1}
  • id: 2280114
    {'lmfdb_iso': '45570.cr', 'p': 97, 'prec': 20, 'unit': 49224831497676113664181389101697732733, 'val': 1}