Elliptic curve data - 73920.dx3

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '73920bt', 'Clabel': '73920bt5', 'Cnumber': 5, 'abc_quality': 1.0656902431070385, 'absD': 1396711936678707855360000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, -1, 0, -28017505, -5002857503], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 73920, 'degree': 10616832, 'elladic_images': ['4.12.0.8', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3226556465507568440507198762', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 101, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [9278380528613437145689, 5328033205714065000], 'lmfdb_iso': '73920.dx', 'lmfdb_label': '73920.dx3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -437774, -9825928], 'min_quad_twist_disc': 8, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.12.0-4.c.1.2', '6.12.0.a.1', '12.48.0-12.g.1.7', '24.96.0-24.bu.1.15', '40.24.0-40.y.1.10', '120.192.1.?', '462.24.0.?', '616.24.0.?', '924.96.0.?', '1848.192.1.?', '3080.48.0.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2829348757108388799248716940', 'prec': 100}, 'szpiro_ratio': 5.624841045219989, '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, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -2, 0, -1, 0, -6, 0, 4, 0], 'aplist': [0, -1, 1, 1, 1, -2, -6, 4, 0, 6, -4, -2, -6, 4, 0, 6, -12, -14, 16, 0, 2, -4, 0, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 73920, 'isogeny_matrix': [[1, 2, 3, 4, 6, 12, 12, 4], [2, 1, 6, 2, 3, 6, 6, 2], [3, 6, 1, 12, 2, 4, 4, 12], [4, 2, 12, 1, 6, 3, 12, 4], [6, 3, 2, 6, 1, 2, 2, 6], [12, 6, 4, 3, 2, 1, 4, 12], [12, 6, 4, 12, 2, 4, 1, 3], [4, 2, 12, 4, 6, 12, 3, 1]], 'lmfdb_iso': '73920.dx', 'trace_hash': 825208650519263587}
• 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': '0.0013001036419682591988014315522', 'prec': 110}, 'conductor': 73920, 'gens': [], 'heights': [], 'lmfdb_label': '73920.dx3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.071281571135472468945806462946', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7107577072513392546993551107047906585', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-5201, 0, 1]], 'xcoord_integral_points': [-5201]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [6, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '73920.dx3'}
• ec_torsion_growth •

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

  
  
  • id: 3496204
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 2]}
  • id: 3496207
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [6]}
  • id: 3496205
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [4]}
  • id: 3496206
    {'degree': 2, 'field': [154, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [4]}
  • id: 3496208
    {'degree': 4, 'field': [-7546, 0, 0, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 4]}
  • id: 3496211
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [12]}
  • id: 3496210
    {'degree': 4, 'field': [287, 42, -41, -2, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 6]}
  • id: 3496212
    {'degree': 4, 'field': [1521, 0, 76, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [12]}
  • id: 3496209
    {'degree': 4, 'field': [5929, 0, 0, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 4]}
  • id: 3496213
    {'degree': 6, 'field': [864, 0, 148, 0, 2, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [6]}
  • id: 3496217
    {'degree': 8, 'field': [23716, 0, 0, 0, -12166, 0, 0, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 12]}
  • id: 3496215
    {'degree': 8, 'field': [23716, 0, 0, 0, 268, 0, 0, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [8]}
  • id: 3496218
    {'degree': 8, 'field': [130321, 0, 0, 0, 799, 0, 0, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 12]}
  • id: 3496216
    {'degree': 8, 'field': [1134896, -286496, 110208, -29120, 3651, 430, -93, -2, 1], 'lmfdb_label': '73920.dx3', 'torsion': [8]}
  • id: 3496214
    {'degree': 8, 'field': [56927025, 0, 90556, 0, -15086, 0, 4, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [4, 4]}
  • id: 3496219
    {'degree': 12, 'field': [9604, 27048, 26390, 4800, -3837, -168, 118, -504, 105, -12, 8, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [3, 6]}
  • id: 3496221
    {'degree': 12, 'field': [11664, 0, 0, 0, 1153, 0, 0, 0, -73, 0, 0, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [12]}
  • id: 3496220
    {'degree': 12, 'field': [119845980, -71160120, 8281320, 455592, -654245, 20342, 93437, -11146, 4798, -170, 113, -2, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 6]}
  • id: 3496222
    {'degree': 12, 'field': [2767286025, 0, 574648200, 0, 33979075, 0, 1168624, 0, 22203, 0, 232, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [12]}
  • id: 3496224
    {'degree': 16, 'field': [1476225, 0, 1229920, 0, 12056, 0, -41032, 0, 12174, 0, 384, 0, -136, 0, 8, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 8]}
  • id: 3496227
    {'degree': 16, 'field': [35153041, 0, 21913584, 0, 6830208, 0, 927696, 0, 18418, 0, -12048, 0, 1152, 0, -48, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [24]}
  • id: 3496226
    {'degree': 16, 'field': [35153041, 0, 140612164, 0, 281224328, 0, 131481504, 0, 29876231, 0, -1707552, 0, 47432, 0, -308, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [4, 12]}
  • id: 3496228
    {'degree': 16, 'field': [423289476, 0, 78149124, 0, 42181093, 0, 8680926, 0, 1254923, 0, 99192, 0, 4427, 0, 102, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [24]}
  • id: 3496225
    {'degree': 16, 'field': [5508903401, -342665864, 586843072, -430645656, 76836154, 150295256, -24537212, -20099504, 2829243, 1360744, -171292, -52288, 6470, 1008, -124, -8, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 8]}
  • id: 3496223
    {'degree': 16, 'field': [896884761600, 0, 5999398912, 0, -4244050944, 0, -233132032, 0, -4308416, 0, 74368, 0, 13664, 0, 192, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [2, 8]}
  • id: 3496229
    {'degree': 18, 'field': [1406386975, -522562950, 259888125, -35891610, 195962190, 697970700, 81583477, -206181972, -44251539, 23335758, 6313665, -1243170, -408281, 29898, 12786, -258, -186, 0, 1], 'lmfdb_label': '73920.dx3', 'torsion': [18]}
• 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: 1792860
    {'conductor': 73920, 'conductor_valuation': 6, 'discriminant_valuation': 21, 'j_denominator_valuation': 3, 'kodaira_symbol': -15, 'lmfdb_label': '73920.dx3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1792861
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '73920.dx3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1792862
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '73920.dx3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1792863
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '73920.dx3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1792864
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '73920.dx3', 'prime': 11, '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: 2152280
    {'adelic_gens': [[3376, 3, 7101, 9154], [2311, 24, 2310, 1], [4998, 6521, 2203, 2548], [1, 12, 12, 145], [4621, 24, 3080, 1541], [15, 106, 7934, 11], [3697, 24, 7404, 289], [1336, 3, 6141, 9154], [9217, 24, 9216, 25], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 73920, 'lmfdb_label': '73920.dx3', 'prime': 0}
  • id: 305879
    {'conductor': 73920, 'elladic_image': '4.12.0.8', 'lmfdb_label': '73920.dx3', 'modell_image': '2B', 'prime': 2}
  • id: 305880
    {'conductor': 73920, 'elladic_image': '3.4.0.1', 'lmfdb_label': '73920.dx3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 73920.dx does not appear in ec_padic