Elliptic curve data - 230115.b4

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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': '230115b', 'Clabel': '230115b1', 'Cnumber': 1, 'abc_quality': 0.910707606543615, 'absD': 72319290500244140625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 80040, 'ainvs': [1, 1, 1, -2777261, 1732668458], 'analytic_rank': 1, 'bad_primes': [3, 5, 23, 29], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 230115, 'degree': 6488064, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5865987356430693846294415368', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [16003198512756001, 488525390625], 'lmfdb_iso': '230115.b', 'lmfdb_label': '230115.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5250, -144690], 'min_quad_twist_disc': -23, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '40.12.0.ba.1', '92.12.0.?', '348.12.0.?', '920.24.0.?', '3480.24.0.?', '4002.6.0.?', '8004.24.0.?', '80040.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '18.268404336320277217349573041', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0188516276784945392260651209', 'prec': 100}, 'szpiro_ratio': 4.5458456085270615, '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, -1, -1, -1, -1, 1, 0, 3, 1, 1, 0, 1, 6, 0, 1, -1, -6, -1, 4, 1], 'aplist': [-1, -1, -1, 0, 0, 6, -6, 4, 0, 1, 4, 2, -6, 4, 0, 2, -8, 2, 12, -12, 6, 8, 4, -2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 230115, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '230115.b', 'trace_hash': 779434612471146514}
• 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': '0.0056664216017106724773590965890', 'prec': 110}, 'conductor': 230115, 'gens': [[84791138, 719289110071, 143]], 'heights': [{'__RealLiteral__': 0, 'data': '18.268404336320277217349573041', 'prec': 100}], 'lmfdb_label': '230115.b4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19344709257290006406394839688', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5339697048073176229541263654575176572', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-1919, 959, 1]], 'xcoord_integral_points': [-1919]}
• lmfdb_label 230115.b4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9978364
    {'degree': 2, 'field': [-500, -1, 1], 'lmfdb_label': '230115.b4', 'torsion': [2, 2]}
  • id: 9978365
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '230115.b4', 'torsion': [4]}
  • id: 9978366
    {'degree': 2, 'field': [22, -1, 1], 'lmfdb_label': '230115.b4', 'torsion': [4]}
  • id: 9978367
    {'degree': 4, 'field': [256, 0, 55, 0, 1], 'lmfdb_label': '230115.b4', 'torsion': [2, 4]}
  • id: 9978371
    {'degree': 8, 'field': [-5509435, 361708, -369772, 16127, -8060, -7, 7, -4, 1], 'lmfdb_label': '230115.b4', 'torsion': [6]}
  • id: 9978369
    {'degree': 8, 'field': [15069, 12768, 3835, 1120, 616, -6, 43, -2, 1], 'lmfdb_label': '230115.b4', 'torsion': [8]}
  • id: 9978368
    {'degree': 8, 'field': [2166784, 0, -600944, 0, -828, 0, -92, 0, 1], 'lmfdb_label': '230115.b4', 'torsion': [2, 4]}
  • id: 9978370
    {'degree': 8, 'field': [37515625, 0, 18074875, 0, 311424, 0, 1051, 0, 1], 'lmfdb_label': '230115.b4', 'torsion': [8]}
  • id: 9978376
    {'degree': 16, 'field': [3222025, 0, 18775228, 0, 3936040, 0, -107379, 0, 2172, 0, 11655, 0, 925, 0, 46, 0, 1], 'lmfdb_label': '230115.b4', 'torsion': [12]}
  • id: 9978372
    {'degree': 16, 'field': [16777216, 0, 0, 0, -15343616, 0, 0, 0, 5565345, 0, 0, 0, -3746, 0, 0, 0, 1], 'lmfdb_label': '230115.b4', 'torsion': [4, 4]}
  • id: 9978373
    {'degree': 16, 'field': [155351296, 0, 146993536, 0, 3890864, 0, 263064, 0, 312329, 0, 36186, 0, 2339, 0, 94, 0, 1], 'lmfdb_label': '230115.b4', 'torsion': [2, 8]}
  • id: 9978377
    {'degree': 16, 'field': [40189446400, 10803315200, 15830917632, 4506618528, -9942912, -204299304, 101555620, 6424472, -1619073, -97416, 53724, -21003, 3920, -161, 51, -4, 1], 'lmfdb_label': '230115.b4', 'torsion': [12]}
  • id: 9978375
    {'degree': 16, 'field': [3911256911943, -4644430581636, -2855225346777, -273490431165, -238941169506, -40041642474, 734621058, 986813433, 18830457, -2038257, -656901, 110469, 6915, 417, -185, -7, 1], 'lmfdb_label': '230115.b4', 'torsion': [2, 6]}
  • id: 9978374
    {'degree': 16, 'field': [37523699994364, 230575106717506, 325135099205463, -65441976642376, 88505358058875, -8498839974234, 4970843532508, -195092692174, 92486687412, -1487852708, 577667932, -4861326, 1604472, -7196, 2061, -4, 1], 'lmfdb_label': '230115.b4', 'torsion': [2, 8]}
• 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: 5706195
    {'conductor': 230115, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '230115.b4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5706196
    {'conductor': 230115, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '230115.b4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5706197
    {'conductor': 230115, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '230115.b4', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5706198
    {'conductor': 230115, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '230115.b4', 'prime': 29, '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: 3130757
    {'adelic_gens': [[32017, 8, 48028, 33], [3476, 80039, 80017, 80034], [1, 0, 8, 1], [1, 8, 0, 1], [80033, 8, 80032, 9], [1, 4, 4, 17], [30019, 30018, 10018, 50035], [26684, 1, 53383, 6], [7, 6, 80034, 80035], [10009, 10008, 50038, 10015], [66244, 1, 60743, 6]], 'adelic_image': '80040.48.0.?', 'conductor': 230115, 'lmfdb_label': '230115.b4', 'prime': 0}
  • id: 839094
    {'conductor': 230115, 'elladic_image': '4.6.0.1', 'lmfdb_label': '230115.b4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 230115.b does not appear in ec_padic