Elliptic curve data - 6050.h4

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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': '6050g', 'Clabel': '6050g2', 'Cnumber': 2, 'abc_quality': 1.0629647337743247, 'absD': 1451262771200, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 1320, 'ainvs': [1, 1, 0, 2660, 25040], 'analytic_rank': 0, 'bad_primes': [2, 5, 11], 'class_deg': 15, 'class_size': 4, 'cm': 0, 'conductor': 6050, 'degree': 8100, 'elladic_images': ['8.2.0.1', '3.4.0.1', '5.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0221541845893585849747690274', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 7, 'isogeny_degrees': [1, 3, 5, 15], 'jinv': [46969655, 32768], 'lmfdb_iso': '6050.h', 'lmfdb_label': '6050.h4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 22, -9], 'min_quad_twist_disc': -11, 'modell_images': ['3B', '5B.4.1'], 'modm_images': ['3.4.0.a.1', '5.12.0.a.1', '8.2.0.a.1', '15.96.1.a.3', '24.8.0.a.1', '40.24.1.bx.1', '55.24.0-5.a.1.1', '120.192.9.?', '165.192.1.?', '440.48.1.?', '1320.384.9.?'], 'nonmax_primes': [2, 3, 5], 'nonmax_rad': 30, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3025], [3, 2, 3025], [5, 10, 121], [11, 62, 50]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.44503310388217674948966265045', 'prec': 107}, 'szpiro_ratio': 4.050529971483988, '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, -1, -1, 1, 0, 1, 2, -1, -2, 0, 0, -1, -4, -2, 0, 1, -3, 2, -5, 0], 'aplist': [-1, -1, 0, 2, 0, -4, -3, -5, -6, 0, 2, -2, 3, -4, -12, -6, 0, -2, 13, 12, 11, 10, -9, 15, -2], 'class_deg': 15, 'class_size': 4, 'conductor': 6050, 'isogeny_matrix': [[1, 3, 15, 5], [3, 1, 5, 15], [15, 5, 1, 3], [5, 15, 3, 1]], 'lmfdb_iso': '6050.h', 'trace_hash': 65846767149951449}
• 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': '0.12946970425627167958679796041', 'prec': 103}, 'conductor': 6050, 'gens': [], 'heights': [], 'lmfdb_label': '6050.h4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.53854188011704719052812505872', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.53854188011704719052812505871967217796', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [0, 0], '5': 'a', '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], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '6050.h4'}
• ec_torsion_growth •

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

  
  
  • id: 315285
    {'degree': 2, 'field': [-41, -1, 1], 'lmfdb_label': '6050.h4', 'torsion': [3]}
  • id: 315286
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '6050.h4', 'torsion': [5]}
  • id: 315287
    {'degree': 3, 'field': [2, 2, -1, 1], 'lmfdb_label': '6050.h4', 'torsion': [2]}
  • id: 315288
    {'degree': 4, 'field': [1, 0, 13, 0, 1], 'lmfdb_label': '6050.h4', 'torsion': [15]}
  • id: 315291
    {'degree': 6, 'field': [-1559, 2319, 1000, 85, 40, -1, 1], 'lmfdb_label': '6050.h4', 'torsion': [6]}
  • id: 315289
    {'degree': 6, 'field': [2, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '6050.h4', 'torsion': [2, 2]}
  • id: 315292
    {'degree': 6, 'field': [5, 25, 30, -13, 12, -1, 1], 'lmfdb_label': '6050.h4', 'torsion': [10]}
  • id: 315290
    {'degree': 6, 'field': [320, 0, 0, -35, 0, 0, 1], 'lmfdb_label': '6050.h4', 'torsion': [3]}
  • id: 315298
    {'degree': 12, 'field': [265, -500, 555, -1270, 2050, -1520, 1659, -542, 410, -60, 35, -2, 1], 'lmfdb_label': '6050.h4', 'torsion': [30]}
  • id: 315297
    {'degree': 12, 'field': [704, -528, 2148, -3770, 3345, -2148, 1431, -726, 330, -110, 33, -6, 1], 'lmfdb_label': '6050.h4', 'torsion': [15]}
  • id: 315294
    {'degree': 12, 'field': [2704, -9672, 5712, 7250, -2025, -1722, 281, 174, 60, -80, 27, -6, 1], 'lmfdb_label': '6050.h4', 'torsion': [3, 3]}
  • id: 315296
    {'degree': 12, 'field': [2891, 3654, 3537, 1610, 216, -50, 345, -90, 116, -30, 13, -2, 1], 'lmfdb_label': '6050.h4', 'torsion': [2, 10]}
  • id: 315293
    {'degree': 12, 'field': [363056, 6605152, -857236, 713960, 331540, -28928, 14814, 748, -910, 120, -1, -2, 1], 'lmfdb_label': '6050.h4', 'torsion': [4]}
  • id: 315295
    {'degree': 12, 'field': [34128964, -958088, 2864802, 1131520, 13295, 15012, 18106, -504, 185, 140, 12, -4, 1], 'lmfdb_label': '6050.h4', 'torsion': [2, 6]}
  • id: 315299
    {'degree': 18, 'field': [-271513079, 103345815, 169394397, -30564824, -32872260, -3842340, -7804080, -2327010, 2042415, 768185, -76503, -22770, 3294, -1998, 300, 166, -45, -3, 1], 'lmfdb_label': '6050.h4', 'torsion': [9]}
  • id: 315300
    {'degree': 18, 'field': [1124864, 0, 0, -709112, 0, 0, 129480, 0, 0, -8975, 0, 0, 1285, 0, 0, -47, 0, 0, 1], 'lmfdb_label': '6050.h4', 'torsion': [6]}
  • id: 315301
    {'degree': 20, 'field': [28629151, 0, 0, 0, 0, 5348406, 0, 0, 0, 0, -64864, 0, 0, 0, 0, -294, 0, 0, 0, 0, 1], 'lmfdb_label': '6050.h4', 'torsion': [5]}
• 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: 120335
    {'conductor': 6050, 'conductor_valuation': 1, 'discriminant_valuation': 15, 'j_denominator_valuation': 15, 'kodaira_symbol': 19, 'lmfdb_label': '6050.h4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 120336
    {'conductor': 6050, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '6050.h4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 120337
    {'conductor': 6050, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '6050.h4', '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: 1703649
    {'adelic_gens': [[881, 440, 880, 441], [1, 1122, 330, 661], [121, 1200, 120, 121], [1, 0, 660, 1], [441, 770, 880, 1057], [661, 330, 165, 331], [119, 0, 0, 1319], [166, 825, 165, 1], [881, 330, 880, 1], [1, 396, 660, 1], [1, 0, 1200, 1], [991, 330, 495, 331], [1, 0, 990, 1], [1, 792, 0, 1]], 'adelic_image': '1320.384.9.?', 'conductor': 6050, 'lmfdb_label': '6050.h4', 'prime': 0}
  • id: 29819
    {'conductor': 6050, 'elladic_image': '8.2.0.1', 'lmfdb_label': '6050.h4', 'modell_image': '2G', 'prime': 2}
  • id: 29820
    {'conductor': 6050, 'elladic_image': '3.4.0.1', 'lmfdb_label': '6050.h4', 'modell_image': '3B', 'prime': 3}
  • id: 29821
    {'conductor': 6050, 'elladic_image': '5.12.0.1', 'lmfdb_label': '6050.h4', 'modell_image': '5B.4.1', 'prime': 5}
• lmfdb_iso 6050.h does not appear in ec_padic