Elliptic curve data - 397800.ef4

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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': '397800ef', 'Clabel': '397800ef1', 'Cnumber': 1, 'abc_quality': 0.9547039170966647, 'absD': 265467354750000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 26520, 'ainvs': [0, 0, 0, -8850, -846875], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 397800, 'degree': 1572864, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4537518417295716675718422263', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 109, 'isogeny_degrees': [1, 2, 4], 'jinv': [-420616192, 1456611], 'lmfdb_iso': '397800.ef', 'lmfdb_label': '397800.ef4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -39, 264], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '60.12.0-4.c.1.2', '102.6.0.?', '104.12.0.?', '204.12.0.?', '340.12.0.?', '1020.24.0.?', '1560.24.0.?', '5304.24.0.?', '8840.24.0.?', '26520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 3825], [3, 8, 44200], [5, 14, 15912], [13, 14, 30600], [17, 18, 23400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.13132231900818180189857076593', 'prec': 107}, 'szpiro_ratio': 3.166022755009039, '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, 4, 0, 0, 0, 4, 0, -1, 0, 0, 0, 1, 0, -4, 0], 'aplist': [0, 0, 0, 4, 4, -1, 1, -4, -8, 2, -4, 6, 6, 4, -4, 14, 0, -10, 12, 8, 10, 8, -8, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 397800, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '397800.ef', 'trace_hash': 15914286406662271}
• 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': '0.054611888411441083468116952165', 'prec': 107}, 'conductor': 397800, 'gens': [], 'heights': [], 'lmfdb_label': '397800.ef4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.22606758775690091095192097342', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6170814041104145752307355746746389609', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[125, 0, 1]], 'xcoord_integral_points': [125]}
• lmfdb_label 397800.ef4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16414147
    {'degree': 2, 'field': [-21, -1, 1], 'lmfdb_label': '397800.ef4', 'torsion': [4]}
  • id: 16414148
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '397800.ef4', 'torsion': [4]}
  • id: 16414146
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '397800.ef4', 'torsion': [2, 2]}
  • id: 16414149
    {'degree': 4, 'field': [69, 33, -2, -1, 1], 'lmfdb_label': '397800.ef4', 'torsion': [2, 4]}
  • id: 16414153
    {'degree': 8, 'field': [-216996, -264992, -108836, -5616, 1820, 416, -264, -2, 1], 'lmfdb_label': '397800.ef4', 'torsion': [6]}
  • id: 16414152
    {'degree': 8, 'field': [1564, -2784, 2764, 28, 17, -40, 18, -4, 1], 'lmfdb_label': '397800.ef4', 'torsion': [8]}
  • id: 16414150
    {'degree': 8, 'field': [76176, 0, -4320, 0, 1452, 0, -60, 0, 1], 'lmfdb_label': '397800.ef4', 'torsion': [2, 4]}
  • id: 16414151
    {'degree': 8, 'field': [6446469, 591720, -582954, -17652, 9127, -364, 126, -4, 1], 'lmfdb_label': '397800.ef4', 'torsion': [8]}
  • id: 16414154
    {'degree': 16, 'field': [36481, 0, 303344, 0, 625738, 0, 71216, 0, 23323, 0, 3632, 0, 382, 0, 32, 0, 1], 'lmfdb_label': '397800.ef4', 'torsion': [4, 4]}
  • id: 16414155
    {'degree': 16, 'field': [2016400, 0, 3682080, 0, 5410444, 0, 72000, 0, -61095, 0, 576, 0, 250, 0, 0, 0, 1], 'lmfdb_label': '397800.ef4', 'torsion': [2, 8]}
  • id: 16414159
    {'degree': 16, 'field': [10434496, -725888, 673344, -387744, 1525152, -1877304, 1098508, -419528, 126045, -19440, 9696, -3792, 1178, -280, 60, -8, 1], 'lmfdb_label': '397800.ef4', 'torsion': [12]}
  • id: 16414158
    {'degree': 16, 'field': [17103769, 281607962, 141920826, -1915898502, 623025936, 783230316, 437532824, 91687270, 10403937, 197596, -31624, 27942, 264, -150, 6, -4, 1], 'lmfdb_label': '397800.ef4', 'torsion': [12]}
  • id: 16414156
    {'degree': 16, 'field': [905056981, -2874391756, 7244490152, -9638052948, 7134849002, -2980819616, 1337604976, -310212924, 97055659, -13480368, 3179704, -270028, 50222, -2436, 368, -8, 1], 'lmfdb_label': '397800.ef4', 'torsion': [2, 8]}
  • id: 16414157
    {'degree': 16, 'field': [99540526698979, 75715358880, 1931985270490, -2817689204894, 88619645338, 4848853174, 6175098002, 976165414, -75237799, 6600656, -1747852, -72886, 14164, -1402, 292, -6, 1], 'lmfdb_label': '397800.ef4', 'torsion': [2, 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: 9841094
    {'conductor': 397800, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '397800.ef4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9841095
    {'conductor': 397800, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '397800.ef4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9841096
    {'conductor': 397800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '397800.ef4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 9841097
    {'conductor': 397800, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '397800.ef4', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9841098
    {'conductor': 397800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '397800.ef4', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 4131848
    {'adelic_gens': [[5303, 0, 0, 26519], [26513, 8, 26512, 9], [24481, 15920, 13060, 10641], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [5971, 5970, 12610, 4651], [7, 6, 26514, 26515], [20561, 25860, 9950, 1991], [19444, 21215, 1745, 26514], [12796, 5305, 11255, 6]], 'adelic_image': '26520.48.0.?', 'conductor': 397800, 'lmfdb_label': '397800.ef4', 'prime': 0}
  • id: 1353461
    {'conductor': 397800, 'elladic_image': '4.6.0.1', 'lmfdb_label': '397800.ef4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 397800.ef does not appear in ec_padic