Elliptic curve data - 78400.fp4

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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
  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': '78400gt', 'Clabel': '78400gt1', 'Cnumber': 1, 'absD': 117649000000, 'ainvs': [0, 0, 0, 1225, 0], 'analytic_rank': 1, 'bad_primes': [2, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': -4, 'conductor': 78400, 'degree': 49152, 'elladic_images': ['16.192.9.178'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.81371469511316997630939701576', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 145, 'isogeny_degrees': [1, 2, 4], 'jinv': [1728, 1], 'lmfdb_iso': '78400.fp', 'lmfdb_label': '78400.fp4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 4, 0], 'min_quad_twist_disc': 280, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.1293250615501705977518991662', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1225], [5, 14, 3136], [7, 26, 1600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3105329259115095182522750833', 'prec': 103}, 'szpiro_ratio': 2.9234180618855823, '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, 0, 0, -6, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, 0, 0, 0, -6, 2, 0, 0, 10, 0, -2, -10, 0, 0, 14, 0, -10, 0, 0, -6, 0, 0, -10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 78400, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '78400.fp', 'trace_hash': 2269761085779168985}
• 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': '0.19643388051486779507114559371', 'prec': 103}, 'conductor': 78400, 'gens': [[225, 3975, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '4.1293250615501705977518991662', 'prec': 100}], 'lmfdb_label': '78400.fp4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.62679164084226234210214205672', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1764528618002147377740235687219198810', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 1, 0], '5': 'a', '7': 'a', '11': [3, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '78400.fp4'}
• ec_torsion_growth •

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

  
  
  • id: 3701656
    {'degree': 2, 'field': [-70, 0, 1], 'lmfdb_label': '78400.fp4', 'torsion': [4]}
  • id: 3701655
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '78400.fp4', 'torsion': [2, 2]}
  • id: 3701657
    {'degree': 2, 'field': [70, 0, 1], 'lmfdb_label': '78400.fp4', 'torsion': [4]}
  • id: 3701658
    {'degree': 4, 'field': [1225, 0, 0, 0, 1], 'lmfdb_label': '78400.fp4', 'torsion': [2, 4]}
  • id: 3701662
    {'degree': 8, 'field': [-4501875, 0, 0, 0, -7350, 0, 0, 0, 1], 'lmfdb_label': '78400.fp4', 'torsion': [6]}
  • id: 3701661
    {'degree': 8, 'field': [4039, -2800, 3326, -1092, 647, -124, 46, -4, 1], 'lmfdb_label': '78400.fp4', 'torsion': [8]}
  • id: 3701659
    {'degree': 8, 'field': [6561, 0, 0, 0, 127, 0, 0, 0, 1], 'lmfdb_label': '78400.fp4', 'torsion': [4, 4]}
  • id: 3701660
    {'degree': 8, 'field': [63224, 6944, -20256, -256, 1948, -8, -76, 0, 1], 'lmfdb_label': '78400.fp4', 'torsion': [8]}
  • id: 3701663
    {'degree': 8, 'field': [75154, 25024, -13612, -3156, 1444, 200, -62, -4, 1], 'lmfdb_label': '78400.fp4', 'torsion': [2, 10]}
  • id: 3701666
    {'degree': 16, 'field': [-25924, -2641504, 340384, 2668784, -939464, -716272, 432256, 6104, -58414, 14504, 1620, -1444, 172, 52, -10, -4, 1], 'lmfdb_label': '78400.fp4', 'torsion': [10]}
  • id: 3701668
    {'degree': 16, 'field': [8120506, -386448, -5548172, -609448, 2662348, -2200, -493716, -54184, 81872, 5940, -6632, -1280, 578, 60, -20, -4, 1], 'lmfdb_label': '78400.fp4', 'torsion': [2, 20]}
  • id: 3701664
    {'degree': 16, 'field': [8854049, 12565316, -5091860, -12673340, 1045348, 5290352, -115880, -1183980, 27157, 154248, -6940, -11700, 858, 476, -48, -8, 1], 'lmfdb_label': '78400.fp4', 'torsion': [4, 8]}
  • id: 3701667
    {'degree': 16, 'field': [5299988766, 1931384760, -2664695196, -814174800, 596335680, 143392512, -75649212, -13780440, 5877448, 785348, -285212, -26656, 8446, 500, -140, -4, 1], 'lmfdb_label': '78400.fp4', 'torsion': [12]}
  • id: 3701669
    {'degree': 16, 'field': [13388459401, -1803619940, 5438620724, -747942900, 992180150, -130223488, 105735208, -12491460, 7163068, -717972, 314548, -24836, 8726, -480, 140, -4, 1], 'lmfdb_label': '78400.fp4', 'torsion': [12]}
  • id: 3701665
    {'degree': 16, 'field': [1428588317881, -447797890076, 64727669186, -27316526424, 513275150, -839733664, 205825510, -15560580, 19525726, -296004, 833086, -16400, 19022, -432, 218, -4, 1], 'lmfdb_label': '78400.fp4', 'torsion': [6, 6]}
• 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: 1908615
    {'conductor': 78400, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '78400.fp4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1908616
    {'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '78400.fp4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1908617
    {'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '78400.fp4', 'prime': 7, '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

  
  {'conductor': 78400, 'elladic_image': '16.192.9.178', 'lmfdb_label': '78400.fp4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4037943
    {'lmfdb_iso': '78400.fp', 'p': 13, 'prec': 20, 'unit': 778124688563399368456, 'val': 1}
  • id: 4037945
    {'lmfdb_iso': '78400.fp', 'p': 17, 'prec': 20, 'unit': 13520969669678032831279, 'val': 1}
  • id: 4037944
    {'lmfdb_iso': '78400.fp', 'p': 29, 'prec': 20, 'unit': 617592624939481022653636527, 'val': 1}
  • id: 4037941
    {'lmfdb_iso': '78400.fp', 'p': 37, 'prec': 20, 'unit': 309318855536438530927823996429, 'val': 1}
  • id: 4037942
    {'lmfdb_iso': '78400.fp', 'p': 41, 'prec': 20, 'unit': 2400957190014411914856346358749, 'val': 1}
  • id: 4037946
    {'lmfdb_iso': '78400.fp', 'p': 53, 'prec': 20, 'unit': 84618600754967814460284924456898, 'val': 1}
  • id: 4037949
    {'lmfdb_iso': '78400.fp', 'p': 61, 'prec': 20, 'unit': 3287220786120595923948856879449618, 'val': 1}
  • id: 4037947
    {'lmfdb_iso': '78400.fp', 'p': 73, 'prec': 20, 'unit': 129171474292728110591808924902614159, 'val': 1}
  • id: 4037948
    {'lmfdb_iso': '78400.fp', 'p': 89, 'prec': 20, 'unit': 1474465841432789303656971908584370187, 'val': 1}
  • id: 4037940
    {'lmfdb_iso': '78400.fp', 'p': 97, 'prec': 20, 'unit': 16592287057675688983013617478100066907, 'val': 1}