Elliptic curve data - 103968.bz4

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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': '103968ca', 'Clabel': '103968ca2', 'Cnumber': 2, 'abc_quality': 1.034713906926563, 'absD': 20595673967325368832, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, 0, 0, -79059, -218514022], 'analytic_rank': 2, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 103968, 'degree': 2211840, 'elladic_images': ['8.12.0.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3851159951748755408061969216', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 51, 'isogeny_degrees': [1, 2, 4], 'jinv': [-3112136, 1172889], 'lmfdb_iso': '103968.bz', 'lmfdb_label': '103968.bz4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -24, 1188], 'min_quad_twist_disc': -228, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.d.1', '24.24.0-8.d.1.3', '152.24.0.?', '228.12.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '29.294931755121794739613614706', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 3249], [3, 8, 11552], [19, 200, 288]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15627002416235851695886350390', 'prec': 107}, 'szpiro_ratio': 4.495203711765108, '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, 2, 0, -4, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, 2, -4, -4, -2, -2, 0, 4, -6, 0, -2, -6, -12, 4, 2, -12, -10, 4, 0, 10, 8, 12, -14, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 103968, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '103968.bz', 'trace_hash': 854334738216620475}
• 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': '0.0084784130217812935633034527452', 'prec': 110}, 'conductor': 103968, 'gens': [[874, 19494, 1], [310609, 173108385, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '2.5784875105701677098251609012', 'prec': 100}, {'__RealLiteral__': 0, 'data': '11.552564293955475109827923512', 'prec': 100}], 'lmfdb_label': '103968.bz4', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.096757821547583944680372975040', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.338055116042898952904760706405474240', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[646, 0, 1]], 'xcoord_integral_points': [646, 874]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [2, 0], '11': [2, 0], '13': [2, 0], '17': [2, 0], '19': 'a', '23': [4, 0], '29': [2, 0], '31': [2, 2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '103968.bz4'}
• ec_torsion_growth •

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

  
  
  • id: 4812543
    {'degree': 2, 'field': [-114, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [4]}
  • id: 4812542
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [2, 2]}
  • id: 4812544
    {'degree': 2, 'field': [57, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [4]}
  • id: 4812545
    {'degree': 4, 'field': [841, 0, -56, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [2, 4]}
  • id: 4812549
    {'degree': 8, 'field': [-87723, 0, 41040, 0, -1026, 0, 0, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [6]}
  • id: 4812548
    {'degree': 8, 'field': [324, 0, -36, 0, 22, 0, 2, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [8]}
  • id: 4812546
    {'degree': 8, 'field': [1024, 0, 0, 0, 178, 0, 0, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [2, 4]}
  • id: 4812547
    {'degree': 8, 'field': [1849, 0, -1308, 0, 122, 0, 12, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [8]}
  • id: 4812550
    {'degree': 16, 'field': [65536, 0, -180224, 0, 247808, 0, -141504, 0, 46577, 0, -8844, 0, 968, 0, -44, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [4, 4]}
  • id: 4812551
    {'degree': 16, 'field': [234256, 0, 375584, 0, 198944, 0, 29568, 0, -5380, 0, -1248, 0, 104, 0, -4, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [2, 8]}
  • id: 4812553
    {'degree': 16, 'field': [535193, -2618392, 9358044, -17624188, 21347062, -9179964, 4771652, -1834828, 441072, -24760, -9740, 1692, -226, -4, 48, -4, 1], 'lmfdb_label': '103968.bz4', 'torsion': [2, 6]}
  • id: 4812552
    {'degree': 16, 'field': [833569, 0, -653504, 0, 193328, 0, -21840, 0, 5015, 0, -960, 0, 128, 0, -8, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [2, 8]}
  • id: 4812554
    {'degree': 16, 'field': [2961178162, -290671736, 43677380, -225965720, -48286920, 25247752, 5458956, 1945240, -534008, -305116, 36660, 11096, -198, 92, -28, -4, 1], 'lmfdb_label': '103968.bz4', 'torsion': [12]}
  • id: 4812555
    {'degree': 16, 'field': [4974198784, 0, 1493442560, 0, 155074048, 0, 3519104, 0, -460940, 0, -29488, 0, 28, 0, 44, 0, 1], 'lmfdb_label': '103968.bz4', 'torsion': [12]}
• 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: 2553727
    {'conductor': 103968, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '103968.bz4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2553728
    {'conductor': 103968, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '103968.bz4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2553729
    {'conductor': 103968, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '103968.bz4', 'prime': 19, '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: 2346491
    {'adelic_gens': [[400, 27, 441, 166], [449, 8, 448, 9], [359, 144, 372, 119], [56, 429, 285, 284], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 450, 451], [151, 0, 0, 455]], 'adelic_image': '456.48.0.?', 'conductor': 103968, 'lmfdb_label': '103968.bz4', 'prime': 0}
  • id: 415860
    {'conductor': 103968, 'elladic_image': '8.12.0.16', 'lmfdb_label': '103968.bz4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 5413453
    {'lmfdb_iso': '103968.bz', 'p': 5, 'prec': 20, 'unit': 9667501250976, 'val': 2}
  • id: 5413454
    {'lmfdb_iso': '103968.bz', 'p': 7, 'prec': 20, 'unit': 5100638761859814, 'val': 2}
  • id: 5413452
    {'lmfdb_iso': '103968.bz', 'p': 11, 'prec': 20, 'unit': 49200909500480566786, 'val': 2}
  • id: 5413458
    {'lmfdb_iso': '103968.bz', 'p': 13, 'prec': 20, 'unit': 953001479080853060958, 'val': 2}
  • id: 5413460
    {'lmfdb_iso': '103968.bz', 'p': 17, 'prec': 20, 'unit': 205378345664736408531187, 'val': 2}
  • id: 5413465
    {'lmfdb_iso': '103968.bz', 'p': 23, 'prec': 20, 'unit': 2326469741776946047327118, 'val': 3}
  • id: 5413457
    {'lmfdb_iso': '103968.bz', 'p': 29, 'prec': 20, 'unit': 1828918311526818061555688692, 'val': 2}
  • id: 5413469
    {'lmfdb_iso': '103968.bz', 'p': 37, 'prec': 20, 'unit': 499064772514438913331159837570, 'val': 2}
  • id: 5413455
    {'lmfdb_iso': '103968.bz', 'p': 41, 'prec': 20, 'unit': 789055464643143969615201341355, 'val': 2}
  • id: 5413456
    {'lmfdb_iso': '103968.bz', 'p': 43, 'prec': 20, 'unit': 106428755446747460093944625057, 'val': 2}
  • id: 5413467
    {'lmfdb_iso': '103968.bz', 'p': 47, 'prec': 20, 'unit': 57607311645862230754228982889772, 'val': 2}
  • id: 5413462
    {'lmfdb_iso': '103968.bz', 'p': 53, 'prec': 20, 'unit': 478183327246822597737241240939259, 'val': 2}
  • id: 5413463
    {'lmfdb_iso': '103968.bz', 'p': 59, 'prec': 20, 'unit': 113272190253881379264329618320388, 'val': 2}
  • id: 5413468
    {'lmfdb_iso': '103968.bz', 'p': 61, 'prec': 20, 'unit': 4527345053563161281231028570645172, 'val': 2}
  • id: 5413461
    {'lmfdb_iso': '103968.bz', 'p': 67, 'prec': 20, 'unit': 3243682579208498441877838677544532, 'val': 2}
  • id: 5413464
    {'lmfdb_iso': '103968.bz', 'p': 73, 'prec': 20, 'unit': 102232153624034797123335862654683635, 'val': 2}
  • id: 5413459
    {'lmfdb_iso': '103968.bz', 'p': 79, 'prec': 20, 'unit': 410738812448967069361090722295667395, 'val': 2}
  • id: 5413451
    {'lmfdb_iso': '103968.bz', 'p': 83, 'prec': 20, 'unit': 623892636238366961592411972036253625, 'val': 2}
  • id: 5413466
    {'lmfdb_iso': '103968.bz', 'p': 89, 'prec': 20, 'unit': 6436947154716776071188639355037056562, 'val': 2}
  • id: 5413450
    {'lmfdb_iso': '103968.bz', 'p': 97, 'prec': 20, 'unit': 38294117256878505878148950969337247512, 'val': 2}