Elliptic curve data - 338.f1

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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': '338c', 'Clabel': '338c3', 'Cnumber': 3, 'abc_quality': 1.0219339430875438, 'absD': 32127240704, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 936, 'ainvs': [1, 0, 0, -77659, -8336303], 'analytic_rank': 0, 'bad_primes': [2, 13], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 338, 'degree': 1008, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3368611048641450237999542315', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 5, 'isogeny_degrees': [1, 3, 9], 'jinv': [-10730978619193, 6656], 'lmfdb_iso': '338.f', 'lmfdb_label': '338.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -460, -3830], 'min_quad_twist_disc': 13, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '24.8.0-3.a.1.7', '39.8.0-3.a.1.2', '72.24.0.?', '104.2.0.?', '117.72.0.?', '312.16.0.?', '936.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 169], [3, 2, 169], [13, 98, 2]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.054386426133376655773210510718', 'prec': 107}, 'szpiro_ratio': 7.795551315202335, '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, 3, 1, 1, 1, -2, 3, -6, 1, 0, 1, 3, 1, -3, -2, -2, 3], 'aplist': [1, 1, 3, 1, -6, 0, -3, -2, 0, 6, 4, 7, 0, -1, -3, 0, 6, 8, -14, 3, -2, 8, -12, 6, 10], 'class_deg': 9, 'class_size': 3, 'conductor': 338, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '338.f', 'trace_hash': 180304324693631673}
• 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': '0.068994933147349855149370583422', 'prec': 107}, 'conductor': 338, 'gens': [], 'heights': [], 'lmfdb_label': '338.f1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14299523481633087937569879280', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5739142266939558287625782703297859741', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [2, 2], '5': [0, 0], '7': [2, 0], '11': [0, 0], '13': 'a', '17': [0, 0], '19': [0, 0], '23': [0, 0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '338.f1'}
• ec_torsion_growth •

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

  
  
  • id: 14670
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '338.f1', 'torsion': [3]}
  • id: 14671
    {'degree': 3, 'field': [-2, -1, 0, 1], 'lmfdb_label': '338.f1', 'torsion': [2]}
  • id: 14673
    {'degree': 6, 'field': [-13, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '338.f1', 'torsion': [3]}
  • id: 14675
    {'degree': 6, 'field': [16, -20, 12, -9, 5, -1, 1], 'lmfdb_label': '338.f1', 'torsion': [6]}
  • id: 14672
    {'degree': 6, 'field': [26, 0, 29, 0, 8, 0, 1], 'lmfdb_label': '338.f1', 'torsion': [2, 2]}
  • id: 14674
    {'degree': 6, 'field': [208, 234, 351, -26, 0, 0, 1], 'lmfdb_label': '338.f1', 'torsion': [9]}
  • id: 14676
    {'degree': 12, 'field': [-16, 112, -28, 264, -228, 28, 119, -90, 25, -8, 11, -6, 1], 'lmfdb_label': '338.f1', 'torsion': [4]}
  • id: 14679
    {'degree': 12, 'field': [64, 0, 26, 0, 217, 0, -68, 0, 22, 0, -6, 0, 1], 'lmfdb_label': '338.f1', 'torsion': [2, 6]}
  • id: 14677
    {'degree': 12, 'field': [144, 72, 216, -570, 285, -48, 115, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '338.f1', 'torsion': [3, 3]}
  • id: 14678
    {'degree': 12, 'field': [351, 0, 0, -234, 0, 0, 88, 0, 0, -14, 0, 0, 1], 'lmfdb_label': '338.f1', 'torsion': [9]}
  • id: 14680
    {'degree': 18, 'field': [2197, 0, 0, -4394, 0, 0, 1859, 0, 0, 2028, 0, 0, 143, 0, 0, -26, 0, 0, 1], 'lmfdb_label': '338.f1', 'torsion': [6]}
  • id: 14681
    {'degree': 18, 'field': [798196464, 0, 678372084, 0, 240123312, 0, 48448413, 0, 6762366, 0, 722475, 0, 55380, 0, 2691, 0, 78, 0, 1], 'lmfdb_label': '338.f1', 'torsion': [18]}
• 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: 3296
    {'conductor': 338, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '338.f1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 3297
    {'conductor': 338, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '338.f1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1667216
    {'adelic_gens': [[1, 18, 0, 1], [1, 0, 18, 1], [10, 9, 81, 73], [919, 18, 918, 19], [488, 927, 81, 860], [235, 486, 0, 443], [478, 9, 225, 928], [10, 9, 459, 928], [1, 18, 10, 181]], 'adelic_image': '936.144.3.?', 'conductor': 338, 'lmfdb_label': '338.f1', 'prime': 0}
  • id: 1436
    {'conductor': 338, 'elladic_image': '9.12.0.1', 'lmfdb_label': '338.f1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 338.f does not appear in ec_padic