Elliptic curve data - 50820.p2

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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': '50820n', 'Clabel': '50820n1', 'Cnumber': 1, 'abc_quality': 0.9046970159326877, 'absD': 2001263207412213360, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 330, 'ainvs': [0, 1, 0, 200094, 58766805], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 50820, 'degree': 855360, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1957985604353888596821104264', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 3], 'jinv': [2134896896, 4822335], 'lmfdb_iso': '50820.p', 'lmfdb_label': '50820.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 1654, -43551], 'min_quad_twist_disc': -11, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '30.8.0.b.1', '33.8.0-3.a.1.2', '330.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1815], [3, 4, 16940], [5, 6, 10164], [7, 8, 7260], [11, 32, 420]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.033496560416568363508586595724', 'prec': 110}, 'szpiro_ratio': 4.549542622490144, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, 4, 0, -1, 0, -3, 0, 4, 0], 'aplist': [0, 1, -1, -1, 0, 4, -3, 4, 9, 0, 5, -10, 0, 10, 9, -3, -6, 13, -4, 12, -2, 1, -12, 12, -10], 'class_deg': 3, 'class_size': 2, 'conductor': 50820, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '50820.p', 'trace_hash': 2071215542896462480}
• 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': '0.012380939564435500179390052229', 'prec': 107}, 'conductor': 50820, 'gens': [], 'heights': [], 'lmfdb_label': '50820.p2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.18221551807506072055376224072', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2798793253510929699677203330353357509', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [0, 0], '7': [0, 0], '11': 'a', '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '50820.p2'}
• ec_torsion_growth •

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

  
  
  • id: 2465837
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '50820.p2', 'torsion': [3]}
  • id: 2465838
    {'degree': 3, 'field': [-9, 4, -1, 1], 'lmfdb_label': '50820.p2', 'torsion': [2]}
  • id: 2465840
    {'degree': 6, 'field': [-198204, -2568, 2566, 3, 1, -3, 1], 'lmfdb_label': '50820.p2', 'torsion': [3]}
  • id: 2465841
    {'degree': 6, 'field': [75, -60, 20, 16, -6, -1, 1], 'lmfdb_label': '50820.p2', 'torsion': [6]}
  • id: 2465839
    {'degree': 6, 'field': [135, -180, 114, -27, -2, -1, 1], 'lmfdb_label': '50820.p2', 'torsion': [2, 2]}
  • id: 2465844
    {'degree': 12, 'field': [841, 0, -258, 0, 399, 0, 256, 0, -21, 0, -3, 0, 1], 'lmfdb_label': '50820.p2', 'torsion': [2, 6]}
  • id: 2465842
    {'degree': 12, 'field': [15645873, 12389328, 3737424, 813396, 213062, -23666, -22916, 1468, 773, 142, -24, -6, 1], 'lmfdb_label': '50820.p2', 'torsion': [4]}
  • id: 2465843
    {'degree': 12, 'field': [39284825616, 508987872, 515186088, -5400264, 6790264, 607446, -406669, 12831, -2556, -9, 8, -3, 1], 'lmfdb_label': '50820.p2', 'torsion': [3, 3]}
  • id: 2465845
    {'degree': 18, 'field': [2003456937, 264343548, 222373455, 193786903, 219392877, 100000611, -3037421, -6688857, 3217707, 855514, 86766, -8061, 19915, 1143, -69, 214, 27, -3, 1], 'lmfdb_label': '50820.p2', 'torsion': [9]}
  • id: 2465846
    {'degree': 18, 'field': [7347870531, 10769268600, 1507338000, -2740058244, 686186403, 212549874, -120683705, 36242012, 121269, -2696252, 911350, -175500, 3922, 7950, -2769, 416, -5, -6, 1], 'lmfdb_label': '50820.p2', 'torsion': [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: 1216227
    {'conductor': 50820, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '50820.p2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1216228
    {'conductor': 50820, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '50820.p2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 1216229
    {'conductor': 50820, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '50820.p2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1216230
    {'conductor': 50820, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '50820.p2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1216231
    {'conductor': 50820, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '50820.p2', 'prime': 11, 'reduction_type': 0, '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: 2002011
    {'adelic_gens': [[4, 3, 9, 7], [67, 66, 231, 199], [276, 121, 253, 144], [119, 0, 0, 329], [1, 6, 0, 1], [3, 4, 8, 11], [1, 0, 6, 1], [325, 6, 324, 7]], 'adelic_image': '330.16.0.?', 'conductor': 50820, 'lmfdb_label': '50820.p2', 'prime': 0}
  • id: 218033
    {'conductor': 50820, 'elladic_image': '3.4.0.1', 'lmfdb_label': '50820.p2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 50820.p does not appear in ec_padic