Elliptic curve data - 78400.fa4

Formats: - HTML - YAML - JSON - 2026-04-20T00:34:25.962142

• 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': '78400v', 'Clabel': '78400v1', 'Cnumber': 1, 'abc_quality': 0.9802957926219806, 'absD': 1404928000000, 'ainvs': [0, 0, 0, -3500, -98000], 'analytic_rank': 2, 'bad_primes': [2, 5, 7], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 78400, 'degree': 73728, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0453013380013457343019161391', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 130, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '78400.fa', 'lmfdb_label': '78400.fa4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': 40, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': True, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '8.3038836606010522259232263775', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 175], [5, 14, 3136], [7, 20, 1600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 3.2395700304745643, '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': 78400, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '78400.fa', 'trace_hash': 1481772271088705487}
• 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': '0.12361261500706366841245492420', 'prec': 103}, 'conductor': 78400, 'gens': [[120, 1100, 1], [84, 448, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.7453248339773072582000452587', 'prec': 100}, {'__RealLiteral__': 0, 'data': '3.1195671664762486631391335670', 'prec': 100}], 'lmfdb_label': '78400.fa4', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.30568342084070347041007275619', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.153438254543010845470511393163920654', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[70, 0, 1]], 'xcoord_integral_points': [70, 84, 120, 294, 870, 1645]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 2, 0], '5': 'a', '7': 'a', '11': [2, 0], '13': [2, 2, 0], '17': [2, 2, 0], '19': [2, 4, 0], '23': [2, 0], '29': [2, 0], '31': [2, 2, 0], '37': [2, 0], '41': [2, 2, 0], '43': [2, 0], '47': [2, 2, 0]}, 'iwp0': 0, 'lmfdb_label': '78400.fa4'}
• ec_torsion_growth •

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

  
  
  • id: 3699843
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 2]}
  • id: 3699844
    {'degree': 4, 'field': [-175, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [4]}
  • id: 3699845
    {'degree': 4, 'field': [700, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 4]}
  • id: 3699846
    {'degree': 6, 'field': [7000, 0, 1400, 0, 70, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [14]}
  • id: 3699849
    {'degree': 8, 'field': [-1470000, 0, 147000, 0, -4200, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [6]}
  • id: 3699847
    {'degree': 8, 'field': [30276, 0, 2104, 0, -344, 0, 4, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [4, 4]}
  • id: 3699848
    {'degree': 8, 'field': [37249, 0, -6002, 0, 570, 0, -34, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 8]}
  • id: 3699850
    {'degree': 12, 'field': [1000000, 0, 100000, 0, 10000, 0, 1000, 0, 100, 0, 10, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 14]}
  • id: 3699851
    {'degree': 16, 'field': [5636, -18136, 1524, 30320, -7422, -10632, 5734, -1532, -555, 1344, -854, 132, 160, -112, 36, -8, 1], 'lmfdb_label': '78400.fa4', 'torsion': [8]}
  • id: 3699852
    {'degree': 16, 'field': [7890481, 0, 0, 0, 110177, 0, 0, 0, -3936, 0, 0, 0, -47, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [4, 8]}
  • id: 3699853
    {'degree': 16, 'field': [288898009, 0, -172987350, 0, 45358259, 0, -7020922, 0, 716270, 0, -49526, 0, 2291, 0, -66, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 16]}
  • id: 3699854
    {'degree': 16, 'field': [2160900000000, 0, 216090000000, 0, 15435000000, 0, 617400000, 0, 19110000, 0, 294000, 0, 4200, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [6, 6]}
  • id: 3699855
    {'degree': 20, 'field': [1848770000000000, 0, 0, 0, 5282200000000, 0, 0, 0, 3773000000, 0, -68600000, 0, 3920000, 0, 98000, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', '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: 1907907
    {'conductor': 78400, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '78400.fa4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1907908
    {'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '78400.fa4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1907909
    {'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '78400.fa4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 78400.fa4 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 4036717
    {'lmfdb_iso': '78400.fa', 'p': 11, 'prec': 20, 'unit': 35679361905533204654, 'val': 2}
  • id: 4036719
    {'lmfdb_iso': '78400.fa', 'p': 23, 'prec': 20, 'unit': 38368826457217918954255383, 'val': 2}
  • id: 4036720
    {'lmfdb_iso': '78400.fa', 'p': 29, 'prec': 20, 'unit': 335613865694526179580200966, 'val': 2}
  • id: 4036713
    {'lmfdb_iso': '78400.fa', 'p': 37, 'prec': 20, 'unit': 175161545738592744098807154873, 'val': 2}
  • id: 4036715
    {'lmfdb_iso': '78400.fa', 'p': 43, 'prec': 20, 'unit': 9460614565682704932049125337997, 'val': 2}
  • id: 4036718
    {'lmfdb_iso': '78400.fa', 'p': 53, 'prec': 20, 'unit': 489972216093277609206541162891041, 'val': 2}
  • id: 4036712
    {'lmfdb_iso': '78400.fa', 'p': 67, 'prec': 20, 'unit': 3834954619107892587517883220129735, 'val': 2}
  • id: 4036714
    {'lmfdb_iso': '78400.fa', 'p': 71, 'prec': 20, 'unit': 127429817149241793996271655870489947, 'val': 2}
  • id: 4036716
    {'lmfdb_iso': '78400.fa', 'p': 79, 'prec': 20, 'unit': 671701800899557995101901736702872366, 'val': 2}