Elliptic curve data - 37004.a1

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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': '37004b', 'Clabel': '37004b2', 'Cnumber': 2, 'abc_quality': 0.9950617979294879, 'absD': 202677719104256, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 1914, 'ainvs': [0, -1, 0, -65037, -6398951], 'analytic_rank': 1, 'bad_primes': [2, 11, 29], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 37004, 'degree': 151200, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5806602335351240514857792877', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [-199794688, 1331], 'lmfdb_iso': '37004.a', 'lmfdb_label': '37004.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -77, -289], 'min_quad_twist_disc': 29, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '22.2.0.a.1', '66.8.0.a.1', '87.8.0.?', '1914.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.89218153255052660144805847449', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 9251], [3, 2, 3364], [11, 12, 3364], [29, 422, 44]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56508580183140983505067814279', 'prec': 107}, 'szpiro_ratio': 4.26600743093, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 0, -3, 0, 2, 0, -2, 0, 1, 0, -4, 0, 3, 0, -6, 0, -8, 0], 'aplist': [0, -1, -3, 2, 1, -4, -6, -8, -3, 0, -5, 1, 0, 10, 0, -6, 3, 4, -1, 15, 4, -2, 6, 9, 7], 'class_deg': 3, 'class_size': 2, 'conductor': 37004, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '37004.a', 'trace_hash': 360137814662625703}
• 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': '0.042369756257675944087510046350', 'prec': 107}, 'conductor': 37004, 'gens': [[735, 18502, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.89218153255052660144805847449', 'prec': 103}], 'lmfdb_label': '37004.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14941906448408430175605479687', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3995607389861732509570927531587230200', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [], 'xcoord_integral_points': [295, 735, 19730775]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 1], '5': [1, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': 'a', '31': [1, 0], '37': [3, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '37004.a1'}
• ec_torsion_growth •

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

  
  
  • id: 1830329
    {'degree': 2, 'field': [22, -1, 1], 'lmfdb_label': '37004.a1', 'torsion': [3]}
  • id: 1830330
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '37004.a1', 'torsion': [2]}
  • id: 1830332
    {'degree': 6, 'field': [-295, -237, 132, 37, -18, -3, 1], 'lmfdb_label': '37004.a1', 'torsion': [3]}
  • id: 1830331
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '37004.a1', 'torsion': [2, 2]}
  • id: 1830333
    {'degree': 6, 'field': [9682, -312, 1432, -47, 67, -1, 1], 'lmfdb_label': '37004.a1', 'torsion': [6]}
  • id: 1830334
    {'degree': 12, 'field': [-23129669, 19166824, -2348186, 925470, 544893, -206256, 35220, -2768, -1251, 84, 2, -2, 1], 'lmfdb_label': '37004.a1', 'torsion': [4]}
  • id: 1830335
    {'degree': 12, 'field': [47524, 0, -63576, 0, 35520, 0, -8581, 0, 975, 0, -51, 0, 1], 'lmfdb_label': '37004.a1', 'torsion': [3, 3]}
  • id: 1830336
    {'degree': 12, 'field': [95219653, -21051714, 29667405, -4854880, 3662614, -443342, 231917, -20060, 7970, -450, 141, -4, 1], 'lmfdb_label': '37004.a1', 'torsion': [2, 6]}
  • id: 1830338
    {'degree': 18, 'field': [-40353607, 0, 0, 2588278, 0, 0, 518959, 0, 0, 40832, 0, 0, 827, 0, 0, -22, 0, 0, 1], 'lmfdb_label': '37004.a1', 'torsion': [6]}
  • id: 1830337
    {'degree': 18, 'field': [787005689553, -527628080655, 547202164176, -227598501282, 128277947187, -36821677647, 15159525082, -3247995963, 1054626732, -177846023, 46485810, -6256611, 1328874, -137475, 23865, -1706, 240, -9, 1], 'lmfdb_label': '37004.a1', 'torsion': [9]}
• 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: 872391
    {'conductor': 37004, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '37004.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 872392
    {'conductor': 37004, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '37004.a1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 872393
    {'conductor': 37004, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '37004.a1', 'prime': 29, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1911233
    {'adelic_gens': [[3, 4, 8, 11], [4, 3, 9, 7], [146, 783, 1363, 1393], [1, 0, 6, 1], [1187, 0, 0, 1913], [1909, 6, 1908, 7], [871, 1392, 435, 349], [1, 6, 0, 1]], 'adelic_image': '1914.16.0.?', 'conductor': 37004, 'lmfdb_label': '37004.a1', 'prime': 0}
  • id: 163574
    {'conductor': 37004, 'elladic_image': '3.4.0.1', 'lmfdb_label': '37004.a1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1822031
    {'lmfdb_iso': '37004.a', 'p': 5, 'prec': 20, 'unit': 18764560536078, 'val': 1}
  • id: 1822032
    {'lmfdb_iso': '37004.a', 'p': 7, 'prec': 20, 'unit': 3208460863319196, 'val': 1}
  • id: 1822036
    {'lmfdb_iso': '37004.a', 'p': 13, 'prec': 20, 'unit': 608586291730735807067, 'val': 1}
  • id: 1822038
    {'lmfdb_iso': '37004.a', 'p': 17, 'prec': 20, 'unit': 6004621390221063101911, 'val': 1}
  • id: 1822028
    {'lmfdb_iso': '37004.a', 'p': 19, 'prec': 20, 'unit': 627763824477621216080125, 'val': 1}
  • id: 1822041
    {'lmfdb_iso': '37004.a', 'p': 23, 'prec': 20, 'unit': 21006288166425163363599634, 'val': 1}
  • id: 1822033
    {'lmfdb_iso': '37004.a', 'p': 31, 'prec': 20, 'unit': 6759714940374758334912620606, 'val': 1}
  • id: 1822046
    {'lmfdb_iso': '37004.a', 'p': 37, 'prec': 20, 'unit': 962259042217903711242906042419, 'val': 0}
  • id: 1822035
    {'lmfdb_iso': '37004.a', 'p': 43, 'prec': 20, 'unit': 9890281096823471917124901602516, 'val': 1}
  • id: 1822040
    {'lmfdb_iso': '37004.a', 'p': 53, 'prec': 20, 'unit': 252943332375612711211427515503856, 'val': 1}
  • id: 1822044
    {'lmfdb_iso': '37004.a', 'p': 59, 'prec': 20, 'unit': 2118370202399199683295736087250990, 'val': 1}
  • id: 1822045
    {'lmfdb_iso': '37004.a', 'p': 61, 'prec': 20, 'unit': 752865175087203700211298028594349, 'val': 1}
  • id: 1822030
    {'lmfdb_iso': '37004.a', 'p': 67, 'prec': 20, 'unit': 43083004402877959143618843622977961, 'val': 1}
  • id: 1822043
    {'lmfdb_iso': '37004.a', 'p': 71, 'prec': 20, 'unit': 146679029568730365401031999619420333, 'val': 1}
  • id: 1822034
    {'lmfdb_iso': '37004.a', 'p': 73, 'prec': 20, 'unit': 141769437245568252120651148412366047, 'val': 1}
  • id: 1822037
    {'lmfdb_iso': '37004.a', 'p': 79, 'prec': 20, 'unit': 634245050530805714394606650389481842, 'val': 1}
  • id: 1822039
    {'lmfdb_iso': '37004.a', 'p': 83, 'prec': 20, 'unit': 2831725008618229974889098555523132337, 'val': 1}
  • id: 1822042
    {'lmfdb_iso': '37004.a', 'p': 89, 'prec': 20, 'unit': 8462056856219631905786244515480800069, 'val': 1}
  • id: 1822029
    {'lmfdb_iso': '37004.a', 'p': 97, 'prec': 20, 'unit': 55868381769500264072292390530706708504, 'val': 1}