Elliptic curve data - 304920.cg4

Formats: - HTML - YAML - JSON - 2024-05-03T06:09:12.324078

• 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': '304920cg', 'Clabel': '304920cg2', 'Cnumber': 2, 'abc_quality': 0.9234875310750043, 'absD': 32805352761350400, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 9240, 'ainvs': [0, 0, 0, -457743, 118882258], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 304920, 'degree': 2621440, 'elladic_images': ['4.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0370162148777468690775802466', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 58, 'isogeny_degrees': [1, 2, 4], 'jinv': [32082281296, 99225], 'lmfdb_iso': '304920.cg', 'lmfdb_label': '304920.cg4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -420, 3168], 'min_quad_twist_disc': 33, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '24.24.0.l.1', '40.24.0.h.2', '56.24.0.h.2', '88.24.0.?', '120.48.0.?', '132.24.0.?', '140.24.0.?', '168.48.0.?', '264.48.0.?', '280.48.0.?', '440.48.0.?', '616.48.0.?', '840.96.1.?', '1320.96.0.?', '1848.96.0.?', '3080.96.0.?', '4620.48.0.?', '9240.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 13, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4002795102697474422949667346', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.17333568622879012159583557515', 'prec': 107}, 'szpiro_ratio': 4.016200253602377, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, -1, 1, 0, 2, 2, -4, 0, -2, 8, -2, 2, -4, 0, 10, 12, -6, 12, 0, 6, 8, 4, -2, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 304920, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '304920.cg', 'trace_hash': 1645979339353872650}
• 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': '0.017008663794833971161232921645', 'prec': 107}, 'conductor': 304920, 'gens': [[429, 1210, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4002795102697474422949667346', 'prec': 100}], 'lmfdb_label': '304920.cg4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.37059991132101320565462475722', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.3030953972896032401787517286725707035', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[374, 0, 1], [407, 0, 1]], 'xcoord_integral_points': [-781, -319, 353, 374, 407, 429, 663, 2189]}
• lmfdb_label 304920.cg4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12885444
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '304920.cg4', 'torsion': [2, 4]}
  • id: 12885446
    {'degree': 4, 'field': [289, 0, -1, 0, 1], 'lmfdb_label': '304920.cg4', 'torsion': [2, 4]}
  • id: 12885445
    {'degree': 4, 'field': [609, -84, 85, -2, 1], 'lmfdb_label': '304920.cg4', 'torsion': [2, 4]}
  • id: 12885450
    {'degree': 8, 'field': [-3557763, 0, 271524, 0, -6534, 0, 0, 0, 1], 'lmfdb_label': '304920.cg4', 'torsion': [2, 6]}
  • id: 12885447
    {'degree': 8, 'field': [289, -1190, 2416, -2522, 1437, -214, 76, -4, 1], 'lmfdb_label': '304920.cg4', 'torsion': [4, 4]}
  • id: 12885449
    {'degree': 8, 'field': [1296, 0, -2016, 0, 625, 0, -56, 0, 1], 'lmfdb_label': '304920.cg4', 'torsion': [2, 8]}
  • id: 12885448
    {'degree': 8, 'field': [1296, 0, -1008, 0, 433, 0, -28, 0, 1], 'lmfdb_label': '304920.cg4', 'torsion': [2, 8]}
  • id: 12885453
    {'degree': 16, 'field': [-22641984, 86838912, -68738112, -35155872, 15140736, 2458728, -131348, -418856, -96867, 115856, -5536, -8496, 506, 392, -36, -8, 1], 'lmfdb_label': '304920.cg4', 'torsion': [2, 12]}
  • id: 12885452
    {'degree': 16, 'field': [1446916, -2850272, 557728, 4392640, -5573050, 1129492, 2976624, -3165650, 1522019, -394510, 51996, -4186, 1085, -280, 52, -4, 1], 'lmfdb_label': '304920.cg4', 'torsion': [2, 8]}
  • id: 12885451
    {'degree': 16, 'field': [167277728016, 0, 62027659008, 0, 13959494640, 0, 1626630768, 0, 97467084, 0, 2882232, 0, 43840, 0, 332, 0, 1], 'lmfdb_label': '304920.cg4', '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: 7551118
    {'conductor': 304920, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '304920.cg4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7551119
    {'conductor': 304920, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '304920.cg4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7551120
    {'conductor': 304920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '304920.cg4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7551121
    {'conductor': 304920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '304920.cg4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7551122
    {'conductor': 304920, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '304920.cg4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 3580186
    {'adelic_gens': [[3367, 4202, 5742, 5875], [9233, 8, 9232, 9], [1, 0, 8, 1], [1, 8, 0, 1], [6719, 0, 0, 9239], [5, 4, 9236, 9237], [4203, 1474, 7568, 221], [3785, 1892, 1892, 4621], [3079, 836, 0, 9239], [1519, 3366, 2178, 5875]], 'adelic_image': '9240.192.1.?', 'conductor': 304920, 'lmfdb_label': '304920.cg4', 'prime': 0}
  • id: 1072965
    {'conductor': 304920, 'elladic_image': '4.12.0.3', 'lmfdb_label': '304920.cg4', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 304920.cg does not appear in ec_padic