Elliptic curve data - 3136.z4

Formats: - HTML - YAML - JSON - 2024-04-24T02:27:22.110307

• 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': '3136y', 'Clabel': '3136y2', 'Cnumber': 2, 'abc_quality': 0.9676277689392396, 'absD': 3022415986688, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 504, 'ainvs': [0, -1, 0, -32993, 2316161], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 3136, 'degree': 6144, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3271645371225493828640616718', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [128787625, 98], 'lmfdb_iso': '3136.z', 'lmfdb_label': '3136.z4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -11, 12], 'min_quad_twist_disc': 56, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '12.24.0-6.a.1.12', '18.36.0.a.1', '24.48.0-24.y.1.2', '28.6.0.c.1', '36.72.0-18.a.1.9', '56.12.0.k.1', '63.36.0.d.2', '72.144.1.?', '84.48.0.?', '126.108.2.?', '168.96.1.?', '252.432.7.?', '504.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8067801500536509076783489259', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.68551130824502523381446288211', 'prec': 107}, 'szpiro_ratio': 5.319508545154686, '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, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, -6, 0, -2, 0], 'aplist': [0, 2, 0, 0, 0, -4, -6, -2, 0, 6, -4, -2, -6, 8, -12, -6, 6, 8, -4, 0, -2, -8, 6, 6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 3136, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '3136.z', 'trace_hash': 1452702164727856560}
• 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': '0.070346019792375433566906829523', 'prec': 107}, 'conductor': 3136, 'gens': [[40, 1029, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.8067801500536509076783489259', 'prec': 100}], 'lmfdb_label': '3136.z4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.79430386774744111092040329201', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.4588726582087160938048192561379793737', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[103, 0, 1]], 'xcoord_integral_points': [40, 103]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [7, 0], '5': [1, 1, 0], '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '3136.z4'}
• ec_torsion_growth •

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

  
  
  • id: 162827
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [6]}
  • id: 162826
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [2, 2]}
  • id: 162828
    {'degree': 4, 'field': [1, 1, 0, -1, 1], 'lmfdb_label': '3136.z4', 'torsion': [4]}
  • id: 162829
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [2, 6]}
  • id: 162831
    {'degree': 6, 'field': [-56, 0, 56, 0, -14, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [18]}
  • id: 162830
    {'degree': 6, 'field': [168, 0, 28, 0, 14, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [6]}
  • id: 162833
    {'degree': 8, 'field': [4, 0, -6, 0, 1, 0, 4, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [2, 4]}
  • id: 162834
    {'degree': 8, 'field': [4, 0, 6, 0, 1, 0, -4, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [12]}
  • id: 162832
    {'degree': 8, 'field': [49, 0, -84, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [2, 4]}
  • id: 162838
    {'degree': 12, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [2, 18]}
  • id: 162837
    {'degree': 12, 'field': [225, 0, 732, 0, 919, 0, 484, 0, 123, 0, 16, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [2, 6]}
  • id: 162836
    {'degree': 12, 'field': [9604, 0, 0, 0, 0, 0, 182, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [18]}
  • id: 162835
    {'degree': 12, 'field': [15876, 0, 10584, 0, 5292, 0, 924, 0, 112, 0, 14, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [3, 6]}
  • id: 162840
    {'degree': 16, 'field': [1, 0, -20, 0, 92, 0, -120, 0, 23, 0, 24, 0, -4, 0, -4, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [2, 12]}
  • id: 162841
    {'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 16, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '3136.z4', 'torsion': [2, 12]}
  • id: 162839
    {'degree': 16, 'field': [8, -8, 13, 44, -82, 74, 32, -172, 223, -216, 175, -132, 86, -42, 16, -4, 1], 'lmfdb_label': '3136.z4', 'torsion': [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: 56344
    {'conductor': 3136, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '3136.z4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 56345
    {'conductor': 3136, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '3136.z4', 'prime': 7, '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: 1684331
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [281, 36, 0, 1], [469, 36, 468, 37], [476, 477, 447, 206], [19, 36, 216, 91], [377, 468, 242, 143], [191, 468, 78, 239], [1, 18, 14, 253]], 'adelic_image': '504.864.21.?', 'conductor': 3136, 'lmfdb_label': '3136.z4', 'prime': 0}
  • id: 15653
    {'conductor': 3136, 'elladic_image': '8.6.0.6', 'lmfdb_label': '3136.z4', 'modell_image': '2B', 'prime': 2}
  • id: 15654
    {'conductor': 3136, 'elladic_image': '9.12.0.1', 'lmfdb_label': '3136.z4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 102523
    {'lmfdb_iso': '3136.z', 'p': 13, 'prec': 20, 'unit': 1116250658723839308173, 'val': 1}
  • id: 102525
    {'lmfdb_iso': '3136.z', 'p': 17, 'prec': 20, 'unit': 213157132094933573568410, 'val': 1}
  • id: 102526
    {'lmfdb_iso': '3136.z', 'p': 19, 'prec': 20, 'unit': 480031886210037673117283, 'val': 1}
  • id: 102522
    {'lmfdb_iso': '3136.z', 'p': 29, 'prec': 20, 'unit': 4705188121303404101587165065, 'val': 1}
  • id: 102533
    {'lmfdb_iso': '3136.z', 'p': 31, 'prec': 20, 'unit': 8209862587365789792996094994, 'val': 1}
  • id: 102519
    {'lmfdb_iso': '3136.z', 'p': 37, 'prec': 20, 'unit': 311306743329725119908839094383, 'val': 1}
  • id: 102520
    {'lmfdb_iso': '3136.z', 'p': 41, 'prec': 20, 'unit': 4302964392254144701421844909840, 'val': 1}
  • id: 102521
    {'lmfdb_iso': '3136.z', 'p': 43, 'prec': 20, 'unit': 1922359821576919384055256163566, 'val': 1}
  • id: 102531
    {'lmfdb_iso': '3136.z', 'p': 47, 'prec': 20, 'unit': 43358881342982107494703195201987, 'val': 1}
  • id: 102527
    {'lmfdb_iso': '3136.z', 'p': 53, 'prec': 20, 'unit': 320659352860988232734745291821167, 'val': 1}
  • id: 102528
    {'lmfdb_iso': '3136.z', 'p': 59, 'prec': 20, 'unit': 1338962609279192990663377746929193, 'val': 1}
  • id: 102532
    {'lmfdb_iso': '3136.z', 'p': 61, 'prec': 20, 'unit': 2084736240707242969695629165762792, 'val': 1}
  • id: 102518
    {'lmfdb_iso': '3136.z', 'p': 67, 'prec': 20, 'unit': 18356101042962279608091580907563717, 'val': 1}
  • id: 102529
    {'lmfdb_iso': '3136.z', 'p': 73, 'prec': 20, 'unit': 158826165936958584248090775396572814, 'val': 1}
  • id: 102524
    {'lmfdb_iso': '3136.z', 'p': 79, 'prec': 20, 'unit': 48971604366337640338246179521477531, 'val': 1}
  • id: 102517
    {'lmfdb_iso': '3136.z', 'p': 83, 'prec': 20, 'unit': 2037341151124892104552573369743822459, 'val': 1}
  • id: 102530
    {'lmfdb_iso': '3136.z', 'p': 89, 'prec': 20, 'unit': 4346143358555812364462383789344371882, 'val': 1}
  • id: 102516
    {'lmfdb_iso': '3136.z', 'p': 97, 'prec': 20, 'unit': 20308948583924674590535585358060894262, 'val': 1}