Elliptic curve data - 1950.k2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1950g', 'Clabel': '1950g4', 'Cnumber': 4, 'abc_quality': 0.9796848210169614, 'absD': 952148437500, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 3120, 'ainvs': [1, 0, 1, -21126, 1179148], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 1950, 'degree': 6144, 'elladic_images': ['16.24.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2222186375362530164341358626', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [66730743078481, 60937500], 'lmfdb_iso': '1950.k', 'lmfdb_label': '1950.k2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -845, 9095], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.3', '20.12.0-4.c.1.2', '24.24.0.by.1', '40.24.0-8.n.1.1', '48.48.0-24.by.1.15', '80.48.0.?', '104.24.0.?', '120.48.0.?', '156.12.0.?', '208.48.0.?', '240.96.0.?', '312.48.0.?', '520.48.0.?', '624.96.0.?', '780.24.0.?', '1040.96.0.?', '1560.96.0.?', '3120.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 975], [3, 4, 650], [5, 18, 78], [13, 14, 150]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.41749968131920282913375619599', 'prec': 103}, 'szpiro_ratio': 5.4765825030354165, '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, 0, -1, 0, -1, 1, 0, 4, 1, -1, 0, 0, 1, 6, -1, 4, 0], 'aplist': [-1, 1, 0, 0, 4, -1, 6, 4, -8, 6, -8, 10, -6, -4, 0, 10, 4, -2, 12, 16, -2, -16, 12, 10, 6], 'class_deg': 8, 'class_size': 6, 'conductor': 1950, 'isogeny_matrix': [[1, 8, 2, 4, 4, 8], [8, 1, 4, 8, 2, 4], [2, 4, 1, 2, 2, 4], [4, 8, 2, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '1950.k', 'trace_hash': 635343229649930485}
• 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': '0.086774951593602052628632462038', 'prec': 107}, 'conductor': 1950, 'gens': [], 'heights': [], 'lmfdb_label': '1950.k2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.87646154031067641056727277906', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7529230806213528211345455581101868795', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[343, -347, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': 'a', '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '1950.k2'}
• ec_torsion_growth •

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

  
  
  • id: 98348
    {'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '1950.k2', 'torsion': [4]}
  • id: 98346
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '1950.k2', 'torsion': [2, 2]}
  • id: 98347
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '1950.k2', 'torsion': [4]}
  • id: 98351
    {'degree': 4, 'field': [19, 14, -13, -2, 1], 'lmfdb_label': '1950.k2', 'torsion': [8]}
  • id: 98350
    {'degree': 4, 'field': [599, 54, -53, -2, 1], 'lmfdb_label': '1950.k2', 'torsion': [8]}
  • id: 98349
    {'degree': 4, 'field': [1405, 80, -79, -2, 1], 'lmfdb_label': '1950.k2', 'torsion': [2, 4]}
  • id: 98354
    {'degree': 8, 'field': [-191, 852, -524, -620, 221, 104, -30, -4, 1], 'lmfdb_label': '1950.k2', 'torsion': [2, 8]}
  • id: 98355
    {'degree': 8, 'field': [-24, 69, -78, 17, -5, -7, 7, -4, 1], 'lmfdb_label': '1950.k2', 'torsion': [6]}
  • id: 98352
    {'degree': 8, 'field': [105, -150, 144, 6, 13, -22, 12, -4, 1], 'lmfdb_label': '1950.k2', 'torsion': [2, 4]}
  • id: 98353
    {'degree': 8, 'field': [2042041, 0, -83740, 0, 2958, 0, 20, 0, 1], 'lmfdb_label': '1950.k2', 'torsion': [8]}
  • id: 98360
    {'degree': 16, 'field': [-78815694, 620279754, -381563127, -439685022, 128628096, 100769094, -19552415, -11158706, 1726809, 664538, -89935, -22098, 2591, 476, -48, -8, 1], 'lmfdb_label': '1950.k2', 'torsion': [2, 6]}
  • id: 98361
    {'degree': 16, 'field': [10000, 0, -16000, 0, 6400, 0, 1875, 0, -1350, 0, -285, 0, 25, 0, -10, 0, 1], 'lmfdb_label': '1950.k2', 'torsion': [12]}
  • id: 98356
    {'degree': 16, 'field': [11025, 0, -7740, 0, 25266, 0, 372, 0, 2899, 0, -164, 0, -6, 0, -8, 0, 1], 'lmfdb_label': '1950.k2', 'torsion': [4, 4]}
  • id: 98358
    {'degree': 16, 'field': [592240896, 0, -1184481792, 0, 597935520, 0, -121485312, 0, 11998324, 0, -613808, 0, 16250, 0, -208, 0, 1], 'lmfdb_label': '1950.k2', 'torsion': [16]}
  • id: 98359
    {'degree': 16, 'field': [592240896, 0, 91113984, 0, 6570720, 0, -22464, 0, -20556, 0, -144, 0, 270, 0, 24, 0, 1], 'lmfdb_label': '1950.k2', 'torsion': [16]}
  • id: 98362
    {'degree': 16, 'field': [738793956, 4295731872, -3876055011, -813359700, 342363150, 75279474, -21839921, -2953808, 931755, -108130, 935, 11208, -1777, -70, 30, -8, 1], 'lmfdb_label': '1950.k2', 'torsion': [12]}
  • id: 98357
    {'degree': 16, 'field': [14579355025, 0, 1556835240, 0, -146532614, 0, -7375068, 0, 738699, 0, 4356, 0, -1346, 0, 12, 0, 1], 'lmfdb_label': '1950.k2', '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: 31694
    {'conductor': 1950, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1950.k2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 31695
    {'conductor': 1950, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1950.k2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 31696
    {'conductor': 1950, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '1950.k2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 31697
    {'conductor': 1950, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1950.k2', 'prime': 13, '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: 1676678
    {'adelic_gens': [[1048, 1, 2159, 10], [1, 16, 0, 1], [15, 2, 3022, 3107], [13, 16, 2604, 2665], [5, 4, 3116, 3117], [1, 0, 16, 1], [1696, 5, 2835, 3106], [623, 3104, 1864, 2991], [3105, 16, 3104, 17], [1178, 791, 1867, 1446]], 'adelic_image': '3120.192.1.?', 'conductor': 1950, 'lmfdb_label': '1950.k2', 'prime': 0}
  • id: 9535
    {'conductor': 1950, 'elladic_image': '16.24.0.11', 'lmfdb_label': '1950.k2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1950.k does not appear in ec_padic