Elliptic curve data - 312050.l2

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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': '312050l', 'Clabel': '312050l1', 'Cnumber': 1, 'abc_quality': 0.8000937907084497, 'absD': 1200244311634937500, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 632, 'ainvs': [1, 1, 0, 152775, -47371375], 'analytic_rank': 2, 'bad_primes': [2, 5, 79], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 312050, 'degree': 4792320, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1524034948912012222892504667', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2], 'jinv': [103823, 316], 'lmfdb_iso': '312050.l', 'lmfdb_label': '312050.l2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 1, 1], 'min_quad_twist_disc': -395, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '158.6.0.?', '632.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '13.480648260443378224936260807', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.83703938755935971209760197065', 'prec': 107}, 'szpiro_ratio': 3.863188894786538, '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, 2, 1, 0, -2, 0, -1, 1, 0, -4, 2, -2, 0, 0, 1, -2, -1, 0, 0], 'aplist': [-1, 2, 0, 0, -4, -2, -2, 0, 0, -8, 8, 4, 10, -2, 0, -8, -14, 0, -8, -8, -6, 0, -12, 6, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 312050, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '312050.l', 'trace_hash': 3144990452260074}
• 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': '0.013503491602148491601724535137', 'prec': 107}, 'conductor': 312050, 'gens': [[3785, 232145, 1], [13999141, 52239161395, 63]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2270268214656594529302873596', 'prec': 100}, {'__RealLiteral__': 0, 'data': '11.056618902461377983669800432', 'prec': 100}], 'lmfdb_label': '312050.l2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.14004093543230014772059905778', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '15.102740741010403484302587242395428695', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[230, -115, 1]], 'xcoord_integral_points': [230, 680, 3785]}
• lmfdb_label 312050.l2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13156845
    {'degree': 2, 'field': [20, -1, 1], 'lmfdb_label': '312050.l2', 'torsion': [2, 2]}
  • id: 13156846
    {'degree': 4, 'field': [-119, -18, 19, -2, 1], 'lmfdb_label': '312050.l2', 'torsion': [4]}
  • id: 13156849
    {'degree': 8, 'field': [-43504, -9011, 9752, -1483, 745, -7, 7, -4, 1], 'lmfdb_label': '312050.l2', 'torsion': [6]}
  • id: 13156848
    {'degree': 8, 'field': [956, -2776, 1224, 1928, 263, 54, 31, -2, 1], 'lmfdb_label': '312050.l2', 'torsion': [2, 4]}
  • id: 13156847
    {'degree': 8, 'field': [16900, -5100, 14345, 2750, 856, 292, 4, -2, 1], 'lmfdb_label': '312050.l2', 'torsion': [2, 4]}
  • id: 13156850
    {'degree': 16, 'field': [-638876, -7445280, -23049072, -29157872, -13065518, 3219480, 3879816, 294168, -322029, -93436, 13282, -120, 1579, -72, 82, -4, 1], 'lmfdb_label': '312050.l2', 'torsion': [8]}
  • id: 13156851
    {'degree': 16, 'field': [280064, -2520268, 8231773, -12988740, 13081684, -9386732, 4562059, -1411498, 268665, 10934, -21043, 4090, 263, -156, 44, -4, 1], 'lmfdb_label': '312050.l2', '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: 7726528
    {'conductor': 312050, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '312050.l2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7726529
    {'conductor': 312050, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '312050.l2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 7726530
    {'conductor': 312050, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '312050.l2', 'prime': 79, '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: 3622565
    {'adelic_gens': [[1, 0, 4, 1], [322, 1, 471, 0], [3, 4, 8, 11], [81, 554, 552, 79], [1, 2, 2, 5], [1, 4, 0, 1], [317, 4, 2, 9], [629, 4, 628, 5]], 'adelic_image': '632.12.0.?', 'conductor': 312050, 'lmfdb_label': '312050.l2', 'prime': 0}
  • id: 1094826
    {'conductor': 312050, 'elladic_image': '8.6.0.1', 'lmfdb_label': '312050.l2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 312050.l does not appear in ec_padic