Elliptic curve data - 5904.m3

Formats: - HTML - YAML - JSON - 2026-07-13T22:30:10.303691

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '5904m', 'Clabel': '5904m1', 'Cnumber': 1, 'abc_quality': 0.9582556017330255, 'absD': 17629249536, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 984, 'ainvs': [0, 0, 0, -1299, 16850], 'analytic_rank': 1, 'bad_primes': [2, 3, 41], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 5904, 'degree': 4608, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.71244829550689630163306469698', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4], 'jinv': [81182737, 5904], 'lmfdb_iso': '5904.m', 'lmfdb_label': '5904.m3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -9, 9], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '12.12.0-4.c.1.1', '24.24.0-8.m.1.6', '82.6.0.?', '164.12.0.?', '328.24.0.?', '492.24.0.?', '984.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6234811978893632661108716440', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 369], [3, 8, 656], [41, 42, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.53000502938710385348179004294', 'prec': 107}, 'szpiro_ratio': 3.814370972334694, '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, 0, 0, 0, 2, 0, -4, 0, 0, 0, -4, 0, 2, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, 0, 2, -4, -4, 2, -2, 4, 0, 6, 8, -2, -1, -4, 12, 6, -4, -10, -12, -12, -6, -12, 12, -2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 5904, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '5904.m', 'trace_hash': 2155107260570862085}
• 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': '0.24053333523066995287521605601', 'prec': 103}, 'conductor': 5904, 'gens': [[7, 90, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6234811978893632661108716440', 'prec': 100}], 'lmfdb_label': '5904.m3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.2043400770445954602547840063', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9104469418930557692476057480223826380', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[25, 0, 1]], 'xcoord_integral_points': [-7, 7, 25]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '5904.m3'}
• ec_torsion_growth •

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

  
  
  • id: 307801
    {'degree': 2, 'field': [-123, 0, 1], 'lmfdb_label': '5904.m3', 'torsion': [4]}
  • id: 307800
    {'degree': 2, 'field': [-10, -1, 1], 'lmfdb_label': '5904.m3', 'torsion': [2, 2]}
  • id: 307802
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '5904.m3', 'torsion': [4]}
  • id: 307803
    {'degree': 4, 'field': [46, 26, -25, -2, 1], 'lmfdb_label': '5904.m3', 'torsion': [2, 4]}
  • id: 307807
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, 25, 0, 1], 'lmfdb_label': '5904.m3', 'torsion': [6]}
  • id: 307806
    {'degree': 8, 'field': [4, 0, 12, 0, 13, 0, -6, 0, 1], 'lmfdb_label': '5904.m3', 'torsion': [8]}
  • id: 307804
    {'degree': 8, 'field': [1681, 0, 0, 0, 41, 0, 0, 0, 1], 'lmfdb_label': '5904.m3', 'torsion': [2, 4]}
  • id: 307805
    {'degree': 8, 'field': [3216, 3264, -2384, -1696, 689, 188, -58, -4, 1], 'lmfdb_label': '5904.m3', 'torsion': [8]}
  • id: 307811
    {'degree': 16, 'field': [-377856, 2015232, -2097152, -108672, -1503488, -1862400, -186936, -86616, -74044, 11400, 584, 1860, 786, -78, 43, -6, 1], 'lmfdb_label': '5904.m3', 'torsion': [2, 6]}
  • id: 307810
    {'degree': 16, 'field': [-55368, -81648, 452472, 113040, -1119188, 553392, 513288, -412064, -48406, 96148, -8698, -8756, 1503, 324, -70, -4, 1], 'lmfdb_label': '5904.m3', 'torsion': [2, 8]}
  • id: 307813
    {'degree': 16, 'field': [324, 0, -864, 0, 576, 0, -783, 0, 630, 0, 21, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '5904.m3', 'torsion': [12]}
  • id: 307808
    {'degree': 16, 'field': [10000, 2000, 200, 9240, -1976, -2252, 3858, -1534, 105, 458, -312, 106, -5, -12, 8, -4, 1], 'lmfdb_label': '5904.m3', 'torsion': [4, 4]}
  • id: 307809
    {'degree': 16, 'field': [14884, 0, 62008, 0, 60824, 0, -2964, 0, -3163, 0, 504, 0, 2, 0, 4, 0, 1], 'lmfdb_label': '5904.m3', 'torsion': [2, 8]}
  • id: 307812
    {'degree': 16, 'field': [186624, 0, -1912896, 0, 3285360, 0, -1938924, 0, 340848, 0, -37728, 0, 2245, 0, -73, 0, 1], 'lmfdb_label': '5904.m3', 'torsion': [12]}
• 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: 116904
    {'conductor': 5904, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '5904.m3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 116905
    {'conductor': 5904, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '5904.m3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 116906
    {'conductor': 5904, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5904.m3', 'prime': 41, '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: 1702628
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 978, 979], [844, 657, 15, 334], [787, 126, 210, 43], [655, 0, 0, 983], [119, 120, 930, 113], [977, 8, 976, 9]], 'adelic_image': '984.48.0.?', 'conductor': 5904, 'lmfdb_label': '5904.m3', 'prime': 0}
  • id: 29121
    {'conductor': 5904, 'elladic_image': '8.12.0.11', 'lmfdb_label': '5904.m3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 227267
    {'lmfdb_iso': '5904.m', 'p': 5, 'prec': 20, 'unit': 3224305391637, 'val': 2}
  • id: 227268
    {'lmfdb_iso': '5904.m', 'p': 7, 'prec': 20, 'unit': 3459964275622527, 'val': 1}
  • id: 227266
    {'lmfdb_iso': '5904.m', 'p': 11, 'prec': 20, 'unit': 20933113328894609987, 'val': 1}
  • id: 227273
    {'lmfdb_iso': '5904.m', 'p': 13, 'prec': 20, 'unit': 550023751641155734838, 'val': 1}
  • id: 227275
    {'lmfdb_iso': '5904.m', 'p': 17, 'prec': 20, 'unit': 188618175981578181914725, 'val': 1}
  • id: 227276
    {'lmfdb_iso': '5904.m', 'p': 19, 'prec': 20, 'unit': 733940439538898228666532, 'val': 1}
  • id: 227272
    {'lmfdb_iso': '5904.m', 'p': 29, 'prec': 20, 'unit': 3682332525681333766969441265, 'val': 1}
  • id: 227269
    {'lmfdb_iso': '5904.m', 'p': 31, 'prec': 20, 'unit': 17725067565730466891316177735, 'val': 1}
  • id: 227284
    {'lmfdb_iso': '5904.m', 'p': 37, 'prec': 20, 'unit': 298578683326657464952431685490, 'val': 1}
  • id: 227271
    {'lmfdb_iso': '5904.m', 'p': 43, 'prec': 20, 'unit': 1760996107223368815848429141561, 'val': 1}
  • id: 227282
    {'lmfdb_iso': '5904.m', 'p': 47, 'prec': 20, 'unit': 7154576938432759381700270732181, 'val': 1}
  • id: 227277
    {'lmfdb_iso': '5904.m', 'p': 53, 'prec': 20, 'unit': 290884575549991050327811351784740, 'val': 1}
  • id: 227278
    {'lmfdb_iso': '5904.m', 'p': 59, 'prec': 20, 'unit': 351154676172429587971028953883780, 'val': 1}
  • id: 227283
    {'lmfdb_iso': '5904.m', 'p': 61, 'prec': 20, 'unit': 3193837006469350472970366581969414, 'val': 1}
  • id: 227265
    {'lmfdb_iso': '5904.m', 'p': 67, 'prec': 20, 'unit': 658646239950243278031646928128530, 'val': 1}
  • id: 227281
    {'lmfdb_iso': '5904.m', 'p': 71, 'prec': 20, 'unit': 145765122189500769510350906080855466, 'val': 1}
  • id: 227270
    {'lmfdb_iso': '5904.m', 'p': 73, 'prec': 20, 'unit': 196687313782458472447228111910820412, 'val': 1}
  • id: 227274
    {'lmfdb_iso': '5904.m', 'p': 79, 'prec': 20, 'unit': 564843462965213805157340733630892927, 'val': 1}
  • id: 227279
    {'lmfdb_iso': '5904.m', 'p': 83, 'prec': 20, 'unit': 2752347730895696204059661194591003492, 'val': 1}
  • id: 227280
    {'lmfdb_iso': '5904.m', 'p': 89, 'prec': 20, 'unit': 6394935158582401392205212663589026357, 'val': 1}
  • id: 227264
    {'lmfdb_iso': '5904.m', 'p': 97, 'prec': 20, 'unit': 473825165316631909572220704069318607, 'val': 1}