Elliptic curve data - 25200.s3

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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': '25200bg', 'Clabel': '25200bg1', 'Cnumber': 1, 'abc_quality': 0.9340053106097008, 'absD': 21528281250000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 0, 0, -16050, -750125], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 25200, 'degree': 73728, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3191614048229966274933060050', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 4], 'jinv': [2508888064, 118125], 'lmfdb_iso': '25200.s', 'lmfdb_label': '25200.s3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -71, -246], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0-4.c.1.1', '24.12.0-4.c.1.3', '42.6.0.a.1', '56.12.0-4.c.1.3', '84.12.0.?', '120.24.0.?', '168.24.0.?', '280.24.0.?', '420.24.0.?', '840.48.0.?'], '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': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.26591275591475684197710698723', 'prec': 107}, 'szpiro_ratio': 4.012393023247453, '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, 0, 0, 0, 0, -1, 0, 0, 0, -4, 0, 6, 0, 0, 0, -2, 0, 8, 0], 'aplist': [0, 0, 0, -1, -4, 6, -2, 8, -4, -6, -4, 2, 2, -12, 0, 2, -4, 6, -4, 8, -6, 16, 4, 18, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 25200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '25200.s', 'trace_hash': 2096535331164743485}
• 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': '0.071481056413937007097414927148', 'prec': 107}, 'conductor': 25200, 'gens': [], 'heights': [], 'lmfdb_label': '25200.s3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.42539849953740659996623763493', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7015939981496263998649505397165790537', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-85, 0, 1]], 'xcoord_integral_points': [-85]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '25200.s3'}
• ec_torsion_growth •

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

  
  
  • id: 1267319
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '25200.s3', 'torsion': [2, 2]}
  • id: 1267321
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '25200.s3', 'torsion': [4]}
  • id: 1267320
    {'degree': 2, 'field': [105, 0, 1], 'lmfdb_label': '25200.s3', 'torsion': [4]}
  • id: 1267322
    {'degree': 4, 'field': [105, 0, 1, -2, 1], 'lmfdb_label': '25200.s3', 'torsion': [2, 4]}
  • id: 1267326
    {'degree': 8, 'field': [-1206, 480, 642, -456, -60, 126, -30, -2, 1], 'lmfdb_label': '25200.s3', 'torsion': [6]}
  • id: 1267325
    {'degree': 8, 'field': [21, -96, 216, -234, 103, -2, -6, -2, 1], 'lmfdb_label': '25200.s3', 'torsion': [8]}
  • id: 1267324
    {'degree': 8, 'field': [169, -276, 373, -176, 44, 50, -12, -4, 1], 'lmfdb_label': '25200.s3', 'torsion': [8]}
  • id: 1267323
    {'degree': 8, 'field': [295, 340, -376, 76, -47, 8, 2, -4, 1], 'lmfdb_label': '25200.s3', 'torsion': [2, 4]}
  • id: 1267329
    {'degree': 16, 'field': [81, 0, 567, 0, 1719, 0, 378, 0, 19, 0, -42, 0, 2, 0, 0, 0, 1], 'lmfdb_label': '25200.s3', 'torsion': [2, 8]}
  • id: 1267328
    {'degree': 16, 'field': [625, 0, 15000, 0, 43450, 0, 47400, 0, 24411, 0, 6312, 0, 814, 0, 48, 0, 1], 'lmfdb_label': '25200.s3', 'torsion': [2, 8]}
  • id: 1267327
    {'degree': 16, 'field': [900, 0, 5760, 0, 10356, 0, 2652, 0, -851, 0, -44, 0, 54, 0, -8, 0, 1], 'lmfdb_label': '25200.s3', 'torsion': [4, 4]}
  • id: 1267330
    {'degree': 16, 'field': [34596, -71424, -170052, -143664, -165200, -155292, -158604, -55296, -81702, -55860, 15092, -2544, 726, -108, 30, 0, 1], 'lmfdb_label': '25200.s3', 'torsion': [2, 6]}
  • id: 1267332
    {'degree': 16, 'field': [944784, 0, 0, 0, -23328, 0, 9504, 0, 13560, 0, -864, 0, 60, 0, 8, 0, 1], 'lmfdb_label': '25200.s3', 'torsion': [12]}
  • id: 1267331
    {'degree': 16, 'field': [1376649, 4688982, 2519028, -10546218, 3575880, 994050, -206208, 199854, 345066, -81930, 62328, -7050, 3768, -198, 100, -2, 1], 'lmfdb_label': '25200.s3', 'torsion': [12]}
• 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: 578534
    {'conductor': 25200, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '25200.s3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 578535
    {'conductor': 25200, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '25200.s3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 578536
    {'conductor': 25200, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '25200.s3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 578537
    {'conductor': 25200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '25200.s3', 'prime': 7, '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: 1832390
    {'adelic_gens': [[833, 8, 832, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 834, 835], [739, 738, 538, 115], [272, 837, 275, 838], [503, 832, 332, 807], [311, 312, 722, 305], [124, 1, 503, 6]], 'adelic_image': '840.48.0.?', 'conductor': 25200, 'lmfdb_label': '25200.s3', 'prime': 0}
  • id: 115012
    {'conductor': 25200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '25200.s3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 25200.s does not appear in ec_padic