Elliptic curve data - 900.b3

Formats: - HTML - YAML - JSON - 2026-06-24T06:46:46.232548

• 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': '900e', 'Clabel': '900e1', 'Cnumber': 1, 'abc_quality': 0.9562146657916117, 'absD': 911250000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, 0, 0, -300, -1375], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 900, 'degree': 288, 'elladic_images': ['4.6.0.3', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.42407500503558506182397620450', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [16384, 5], 'lmfdb_iso': '900.b', 'lmfdb_label': '900.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1, 0], 'min_quad_twist_disc': -15, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.b.1', '6.24.0-6.a.1.3', '10.6.0.a.1', '12.48.0-12.f.1.3', '15.8.0-3.a.1.1', '20.24.0.e.1', '24.96.0-24.bq.1.7', '30.48.0-30.a.1.3', '60.192.3-60.bk.1.4', '120.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.32622126681710140134386816381', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 2, 100], [5, 18, 36]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1609991557021684076464367877', 'prec': 103}, 'szpiro_ratio': 4.2227702825430375, '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, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 0, -2, 0, -2, -6, -4, 6, -6, -4, -2, -6, 10, -6, -6, -12, 2, -2, 12, -2, 8, 6, 6, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 900, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '900.b', 'trace_hash': 683769149137015578}
• 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': '0.42820637712534201167782961302', 'prec': 103}, 'conductor': 900, 'gens': [[-10, 25, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.32622126681710140134386816381', 'prec': 103}], 'lmfdb_label': '900.b3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.1743738589880777539284822757', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2986343679758723780425031139164268971', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-5, 0, 1]], 'xcoord_integral_points': [-14, -10, -5, 20, 40, 284]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '900.b3'}
• ec_torsion_growth •

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

  
  
  • id: 42967
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '900.b3', 'torsion': [2, 2]}
  • id: 42968
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '900.b3', 'torsion': [6]}
  • id: 42970
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '900.b3', 'torsion': [2, 6]}
  • id: 42969
    {'degree': 4, 'field': [13, 2, -4, -2, 1], 'lmfdb_label': '900.b3', 'torsion': [4]}
  • id: 42971
    {'degree': 6, 'field': [1, -1, 0, -5, 0, -1, 1], 'lmfdb_label': '900.b3', 'torsion': [2, 6]}
  • id: 42974
    {'degree': 8, 'field': [4, 0, -16, 0, 17, 0, -2, 0, 1], 'lmfdb_label': '900.b3', 'torsion': [12]}
  • id: 42972
    {'degree': 8, 'field': [25, -50, 50, -30, 14, -6, 2, -2, 1], 'lmfdb_label': '900.b3', 'torsion': [2, 4]}
  • id: 42973
    {'degree': 8, 'field': [76, 144, 48, -40, -14, 0, -8, -2, 1], 'lmfdb_label': '900.b3', 'torsion': [2, 4]}
  • id: 42975
    {'degree': 12, 'field': [1, -1, 1, 10, -5, -1, 26, -1, -5, 10, 1, -1, 1], 'lmfdb_label': '900.b3', 'torsion': [6, 6]}
  • id: 42976
    {'degree': 16, 'field': [1, -14, 98, -506, 1533, -1654, 940, -100, -274, 320, -190, 44, 28, -34, 18, -6, 1], 'lmfdb_label': '900.b3', 'torsion': [4, 4]}
  • id: 42978
    {'degree': 16, 'field': [1, -2, 2, -8, 10, -2, 16, -18, 3, -18, 16, -2, 10, -8, 2, -2, 1], 'lmfdb_label': '900.b3', 'torsion': [2, 12]}
  • id: 42979
    {'degree': 16, 'field': [1, 6, 32, 40, 65, -16, 36, -50, 24, -70, 4, -28, 25, 0, 8, -2, 1], 'lmfdb_label': '900.b3', 'torsion': [2, 12]}
  • id: 42977
    {'degree': 16, 'field': [169, -1040, 2180, -2320, 2818, -3244, 2852, -2308, 1688, -1144, 788, -464, 222, -84, 20, -4, 1], 'lmfdb_label': '900.b3', 'torsion': [8]}
  • id: 42980
    {'degree': 18, 'field': [184, 264, 336, 108, 132, 48, 118, -54, 234, -83, 123, -27, 46, -6, 27, -1, 9, 0, 1], 'lmfdb_label': '900.b3', 'torsion': [18]}
• 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: 12043
    {'conductor': 900, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '900.b3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 12044
    {'conductor': 900, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '900.b3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 12045
    {'conductor': 900, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '900.b3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1670263
    {'adelic_gens': [[1, 12, 12, 25], [97, 24, 96, 25], [105, 22, 2, 83], [1, 0, 24, 1], [39, 116, 20, 39], [21, 4, 20, 101], [1, 24, 0, 1], [7, 24, 12, 7], [61, 24, 72, 49], [8, 99, 45, 14]], 'adelic_image': '120.384.9.?', 'conductor': 900, 'lmfdb_label': '900.b3', 'prime': 0}
  • id: 4196
    {'conductor': 900, 'elladic_image': '4.6.0.3', 'lmfdb_label': '900.b3', 'modell_image': '2B', 'prime': 2}
  • id: 4197
    {'conductor': 900, 'elladic_image': '3.4.0.1', 'lmfdb_label': '900.b3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 19368
    {'lmfdb_iso': '900.b', 'p': 7, 'prec': 20, 'unit': 8383101822067157, 'val': 1}
  • id: 19372
    {'lmfdb_iso': '900.b', 'p': 13, 'prec': 20, 'unit': 726632161144723741416, 'val': 1}
  • id: 19374
    {'lmfdb_iso': '900.b', 'p': 17, 'prec': 20, 'unit': 236017252035499134078094, 'val': 1}
  • id: 19375
    {'lmfdb_iso': '900.b', 'p': 19, 'prec': 20, 'unit': 1074951320390009362201675, 'val': 1}
  • id: 19379
    {'lmfdb_iso': '900.b', 'p': 23, 'prec': 20, 'unit': 39333157159467762039914024, 'val': 1}
  • id: 19371
    {'lmfdb_iso': '900.b', 'p': 29, 'prec': 20, 'unit': 3250663076982221702664554765, 'val': 1}
  • id: 19384
    {'lmfdb_iso': '900.b', 'p': 31, 'prec': 20, 'unit': 11505006173508288924638455640, 'val': 1}
  • id: 19367
    {'lmfdb_iso': '900.b', 'p': 37, 'prec': 20, 'unit': 92783927078704444607789517411, 'val': 1}
  • id: 19369
    {'lmfdb_iso': '900.b', 'p': 41, 'prec': 20, 'unit': 2996778711963461102254055767796, 'val': 1}
  • id: 19370
    {'lmfdb_iso': '900.b', 'p': 43, 'prec': 20, 'unit': 5302824452987540815062891462554, 'val': 1}
  • id: 19382
    {'lmfdb_iso': '900.b', 'p': 47, 'prec': 20, 'unit': 3273121931302772814581993894452, 'val': 1}
  • id: 19376
    {'lmfdb_iso': '900.b', 'p': 53, 'prec': 20, 'unit': 116406221714359080194455229736336, 'val': 1}
  • id: 19377
    {'lmfdb_iso': '900.b', 'p': 59, 'prec': 20, 'unit': 3434820268925228339248459464821451, 'val': 1}
  • id: 19383
    {'lmfdb_iso': '900.b', 'p': 61, 'prec': 20, 'unit': 1459479119981947088674023326481787, 'val': 1}
  • id: 19366
    {'lmfdb_iso': '900.b', 'p': 67, 'prec': 20, 'unit': 37134044328447653714147033515722714, 'val': 1}
  • id: 19381
    {'lmfdb_iso': '900.b', 'p': 71, 'prec': 20, 'unit': 43900777651761656721814335261256366, 'val': 1}
  • id: 19378
    {'lmfdb_iso': '900.b', 'p': 73, 'prec': 20, 'unit': 230312422505317130045676620039829889, 'val': 1}
  • id: 19373
    {'lmfdb_iso': '900.b', 'p': 79, 'prec': 20, 'unit': 348471987970435477618323029978242392, 'val': 1}
  • id: 19365
    {'lmfdb_iso': '900.b', 'p': 83, 'prec': 20, 'unit': 1087920701093491515610075463499117181, 'val': 1}
  • id: 19380
    {'lmfdb_iso': '900.b', 'p': 89, 'prec': 20, 'unit': 6783833146886137291684169417243794395, 'val': 1}
  • id: 19364
    {'lmfdb_iso': '900.b', 'p': 97, 'prec': 20, 'unit': 11042012261550028249372421409967769114, 'val': 1}