Elliptic curve data - 137904.cu4

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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': '137904o', 'Clabel': '137904o1', 'Cnumber': 1, 'abc_quality': 0.85449985979477, 'absD': 3355626037051392, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5304, 'ainvs': [0, 1, 0, 22928, -2438188], 'analytic_rank': 0, 'bad_primes': [2, 3, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 137904, 'degree': 516096, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6629231258991108348300836080', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 72, 'isogeny_degrees': [1, 2, 4], 'jinv': [67419143, 169728], 'lmfdb_iso': '137904.cu', 'lmfdb_label': '137904.cu4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 9, 21], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '104.24.0.?', '408.24.0.?', '1326.6.0.?', '2652.24.0.?', '5304.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.31269873339160284261389223424', 'prec': 107}, 'szpiro_ratio': 3.628680089140665, '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, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0], 'aplist': [0, 1, 2, 0, 0, 0, 1, 0, 0, -2, 8, -10, 6, 4, -8, -2, -4, -10, 8, -12, -6, 8, 12, 10, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 137904, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '137904.cu', 'trace_hash': 2079273536529568533}
• 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': '0.035942089821832998439663072250', 'prec': 107}, 'conductor': 137904, 'gens': [], 'heights': [], 'lmfdb_label': '137904.cu4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.23036735020577221728643511509', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6858776032923554765829618413925233904', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[82, 0, 1]], 'xcoord_integral_points': [82]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '13': 'a', '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '137904.cu4'}
• ec_torsion_growth •

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

  
  
  • id: 6238611
    {'degree': 2, 'field': [-663, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [4]}
  • id: 6238612
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [4]}
  • id: 6238610
    {'degree': 2, 'field': [166, -1, 1], 'lmfdb_label': '137904.cu4', 'torsion': [2, 2]}
  • id: 6238613
    {'degree': 4, 'field': [5866, -1699, 249, -1, 1], 'lmfdb_label': '137904.cu4', 'torsion': [2, 4]}
  • id: 6238614
    {'degree': 4, 'field': [27556, 0, -331, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [2, 4]}
  • id: 6238618
    {'degree': 8, 'field': [-8112, 0, 4004, 0, -312, 0, 0, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [6]}
  • id: 6238617
    {'degree': 8, 'field': [1849, 0, -394, 0, -37, 0, 14, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [8]}
  • id: 6238616
    {'degree': 8, 'field': [2704, 0, -8632, 0, 465, 0, 38, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [8]}
  • id: 6238615
    {'degree': 8, 'field': [34409956, 0, -34667, 0, 70335, 0, -497, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [4, 4]}
  • id: 6238623
    {'degree': 16, 'field': [-2770218603, 1309673232, 1563074892, -225526752, -263495148, -22160520, 20956320, 4177920, -571638, -203136, 27052, 7200, -564, -328, -24, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [12]}
  • id: 6238624
    {'degree': 16, 'field': [4761, 0, 57444, 0, -109904, 0, 52128, 0, 966, 0, -732, 0, 48, 0, 24, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [12]}
  • id: 6238619
    {'degree': 16, 'field': [65536, 0, -131072, 0, -55040, 0, 112384, 0, 124000, 0, 7024, 0, -215, 0, -32, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [2, 8]}
  • id: 6238622
    {'degree': 16, 'field': [589824, 0, 1250304, 0, 1767424, 0, 156288, 0, 7680, 0, -1628, 0, -192, 0, 0, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [2, 6]}
  • id: 6238620
    {'degree': 16, 'field': [9566649, 0, 3503700, 0, 3550602, 0, 301512, 0, -9101, 0, -14552, 0, 1650, 0, -68, 0, 1], 'lmfdb_label': '137904.cu4', 'torsion': [2, 8]}
  • id: 6238621
    {'degree': 16, 'field': [10738729, 0, 966884, 0, -212566, 0, -70632, 0, 8339, 0, 504, 0, -94, 0, -4, 0, 1], 'lmfdb_label': '137904.cu4', '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: 3404037
    {'conductor': 137904, 'conductor_valuation': 4, 'discriminant_valuation': 20, 'j_denominator_valuation': 8, 'kodaira_symbol': -16, 'lmfdb_label': '137904.cu4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3404038
    {'conductor': 137904, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '137904.cu4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3404039
    {'conductor': 137904, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '137904.cu4', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 3404040
    {'conductor': 137904, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '137904.cu4', 'prime': 17, '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: 2560564
    {'adelic_gens': [[667, 666, 2002, 4651], [1, 0, 8, 1], [7, 6, 5298, 5299], [1, 8, 0, 1], [1, 4, 4, 17], [1772, 1, 3559, 6], [655, 660, 658, 3313], [5297, 8, 5296, 9], [400, 5301, 4891, 5302], [2188, 1, 647, 6]], 'adelic_image': '5304.48.0.?', 'conductor': 137904, 'lmfdb_label': '137904.cu4', 'prime': 0}
  • id: 533663
    {'conductor': 137904, 'elladic_image': '4.12.0.8', 'lmfdb_label': '137904.cu4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 137904.cu does not appear in ec_padic