Elliptic curve data - 784.f4

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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': '784h', 'Clabel': '784h1', 'Cnumber': 1, 'abc_quality': 0.9802957926219806, 'absD': 1404928, 'ainvs': [0, 0, 0, -35, 98], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 784, 'degree': 64, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.10599120849567710770707958827', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '784.f', 'lmfdb_label': '784.f4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': -4, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.43158104789063939599289247251', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 7], [7, 20, 16]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 3.4051152061126158, '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, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, 0, 0, -4, 0, 0, 0, -8, 2, 0, -6, 0, 12, 0, -10, 0, 0, -4, -16, 0, -8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 784, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '784.f', 'trace_hash': 1925096974840538534}
• 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': '1.2361261500706366841245492420', 'prec': 100}, 'conductor': 784, 'gens': [[1, 8, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.43158104789063939599289247251', 'prec': 103}], 'lmfdb_label': '784.f4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.5575309899160994790492257969', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2075638092815490228323972856988268101', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-7, 0, 1]], 'xcoord_integral_points': [-7, 1, 2, 7, 193]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 5, 0], '5': [3, 1, 0], '7': 'a', '11': [1, 0], '13': [1, 1, 0], '17': [1, 1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '784.f4'}
• ec_torsion_growth •

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

  
  
  • id: 36557
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '784.f4', 'torsion': [2, 2]}
  • id: 36558
    {'degree': 4, 'field': [-3, -4, 5, -2, 1], 'lmfdb_label': '784.f4', 'torsion': [4]}
  • id: 36559
    {'degree': 4, 'field': [2, -4, 3, -1, 1], 'lmfdb_label': '784.f4', 'torsion': [2, 4]}
  • id: 36560
    {'degree': 6, 'field': [-7, 0, 14, 0, -7, 0, 1], 'lmfdb_label': '784.f4', 'torsion': [14]}
  • id: 36563
    {'degree': 8, 'field': [-147, 0, -147, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '784.f4', 'torsion': [6]}
  • id: 36561
    {'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '784.f4', 'torsion': [4, 4]}
  • id: 36562
    {'degree': 8, 'field': [4, 4, -6, 6, 7, -12, 11, -4, 1], 'lmfdb_label': '784.f4', 'torsion': [2, 8]}
  • id: 36565
    {'degree': 12, 'field': [1, -2, -4, -4, -2, 8, 7, 8, -2, -4, -4, -2, 1], 'lmfdb_label': '784.f4', 'torsion': [28]}
  • id: 36564
    {'degree': 12, 'field': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'lmfdb_label': '784.f4', 'torsion': [2, 14]}
  • id: 36566
    {'degree': 16, 'field': [1, -4, -26, 8, 83, -104, -40, 108, -56, -80, -10, 12, 3, -4, -4, 0, 1], 'lmfdb_label': '784.f4', 'torsion': [8]}
  • id: 36567
    {'degree': 16, 'field': [1, 0, 0, 0, -3, 0, 0, 0, 20, 0, 0, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '784.f4', 'torsion': [4, 8]}
  • id: 36568
    {'degree': 16, 'field': [16, 32, 64, -56, -104, -72, -42, 138, 53, 0, 12, -46, 33, -4, 0, -2, 1], 'lmfdb_label': '784.f4', 'torsion': [2, 16]}
  • id: 36569
    {'degree': 16, 'field': [21609, 0, -21609, 0, 15435, 0, -6174, 0, 1911, 0, -294, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '784.f4', 'torsion': [6, 6]}
  • id: 36570
    {'degree': 20, 'field': [184877, 0, 0, 0, 52822, 0, 0, 0, 3773, 0, 686, 0, 392, 0, -98, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '784.f4', 'torsion': [2, 22]}
• 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: 10006
    {'conductor': 784, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '784.f4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 10007
    {'conductor': 784, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '784.f4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 784.f4 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 15391
    {'lmfdb_iso': '784.f', 'p': 11, 'prec': 20, 'unit': 16665631306048683212, 'val': 1}
  • id: 15393
    {'lmfdb_iso': '784.f', 'p': 23, 'prec': 20, 'unit': 30789279185808561224168365, 'val': 1}
  • id: 15394
    {'lmfdb_iso': '784.f', 'p': 29, 'prec': 20, 'unit': 4436627510534004920784072640, 'val': 1}
  • id: 15387
    {'lmfdb_iso': '784.f', 'p': 37, 'prec': 20, 'unit': 292628498591476835425695565474, 'val': 1}
  • id: 15389
    {'lmfdb_iso': '784.f', 'p': 43, 'prec': 20, 'unit': 1674526178197229464382534340443, 'val': 1}
  • id: 15392
    {'lmfdb_iso': '784.f', 'p': 53, 'prec': 20, 'unit': 162871177538534627959209526944053, 'val': 1}
  • id: 15386
    {'lmfdb_iso': '784.f', 'p': 67, 'prec': 20, 'unit': 690221634874592230448587292039078, 'val': 2}
  • id: 15388
    {'lmfdb_iso': '784.f', 'p': 71, 'prec': 20, 'unit': 23820914057084862088732281985833737, 'val': 1}
  • id: 15390
    {'lmfdb_iso': '784.f', 'p': 79, 'prec': 20, 'unit': 866420445257734544436474028981344443, 'val': 1}