Elliptic curve data - 3360.p4

Formats: - HTML - YAML - JSON - 2023-05-29T15:32:48.690210

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '3360k', 'Clabel': '3360k4', 'Cnumber': 4, 'absD': 448270925760000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 1, 0, -17416, 1343384], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3360, 'degree': 15360, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5102570373606597235040814407', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [-1141100604753992, 875529151875], 'lmfdb_iso': '3360.p', 'lmfdb_label': '3360.p4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -17416, 1343384], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['1.1.0.1', '2.3.0.1', '4.6.0.1', '8.12.0.8', '12.12.0.8', '24.24.0.187', '40.24.0.179', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 13, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.19707496030889802440026323516', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.99039665194070074144115734961', 'prec': 103}, '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, -1, 0, 1, 0, 1, 0, -4, 0, -6, 0, -1, 0, 6, 0, 0, 0], 'aplist': [0, 1, -1, 1, -4, -6, 6, 0, 4, -6, 0, 2, 2, -4, -4, -6, -12, -10, -4, -8, -14, -8, 12, -6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 3360, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3360.p', 'trace_hash': 685386152747621251}
• 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': '0.048776137336596387151461839503', 'prec': 107}, 'conductor': 3360, 'gens': [[14, 1050, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.19707496030889802440026323516', 'prec': 103}], 'lmfdb_label': '3360.p4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.48504392907055332565355415423', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8236005227860498107310595970771997616', 'prec': 130}, 'tamagawa_product': 160, 'torsion_generators': [[-161, 0, 1]], 'xcoord_integral_points': [-161, -154, 14, 35, 182, 239, 8414]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [6, 0], '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '3360.p4'}
• ec_torsion_growth •

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

  
  
  • id: 175239
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [4]}
  • id: 175240
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '3360.p4', 'torsion': [4]}
  • id: 175238
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [2, 2]}
  • id: 175241
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [2, 4]}
  • id: 175245
    {'degree': 8, 'field': [-4107, -420, 1662, 340, -304, -32, 22, -4, 1], 'lmfdb_label': '3360.p4', 'torsion': [6]}
  • id: 175244
    {'degree': 8, 'field': [36, 0, -36, 0, 42, 0, 6, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [8]}
  • id: 175243
    {'degree': 8, 'field': [71, 68, -54, -16, -21, 32, -6, -4, 1], 'lmfdb_label': '3360.p4', 'torsion': [8]}
  • id: 175242
    {'degree': 8, 'field': [81, 0, -108, 0, 60, 0, -12, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [2, 4]}
  • id: 175246
    {'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [4, 4]}
  • id: 175247
    {'degree': 16, 'field': [256, 0, 1280, 0, 2912, 0, 3360, 0, 2228, 0, 840, 0, 182, 0, 20, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [2, 8]}
  • id: 175248
    {'degree': 16, 'field': [2401, -7448, 12768, -2620, -10254, 10116, -1628, -1912, 1521, -764, 208, 48, -24, -20, 12, -4, 1], 'lmfdb_label': '3360.p4', 'torsion': [2, 8]}
  • id: 175249
    {'degree': 16, 'field': [149769, 0, 712908, 0, 881100, 0, 442044, 0, 50850, 0, -564, 0, -180, 0, 12, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [2, 6]}
  • id: 175251
    {'degree': 16, 'field': [455625, 0, 0, 0, -60750, 0, -43200, 0, 8775, 0, 2880, 0, 1114, 0, -32, 0, 1], 'lmfdb_label': '3360.p4', 'torsion': [12]}
  • id: 175250
    {'degree': 16, 'field': [15327225, 0, -16139088, 0, 4204980, 0, 236944, 0, -99538, 0, -4400, 0, 100, 0, -16, 0, 1], 'lmfdb_label': '3360.p4', '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: 61183
    {'conductor': 3360, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3360.p4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 61184
    {'conductor': 3360, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '3360.p4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 61185
    {'conductor': 3360, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '3360.p4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 61186
    {'conductor': 3360, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '3360.p4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 1685857
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [49, 48, 118, 55], [88, 3, 85, 2], [113, 8, 112, 9], [7, 6, 114, 115], [97, 8, 28, 33], [1, 4, 4, 17], [48, 113, 67, 54]], 'adelic_image': '120.48.0.?', 'conductor': 3360, 'lmfdb_label': '3360.p4', 'prime': 0}
  • id: 16849
    {'conductor': 3360, 'elladic_image': '8.12.0.8', 'lmfdb_label': '3360.p4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 111666
    {'lmfdb_iso': '3360.p', 'p': 11, 'prec': 20, 'unit': 37060968758814195326, 'val': 1}
  • id: 111672
    {'lmfdb_iso': '3360.p', 'p': 13, 'prec': 20, 'unit': 620434065272344358571, 'val': 1}
  • id: 111674
    {'lmfdb_iso': '3360.p', 'p': 17, 'prec': 20, 'unit': 92417823439799996309832, 'val': 1}
  • id: 111679
    {'lmfdb_iso': '3360.p', 'p': 23, 'prec': 20, 'unit': 23070356214673323838270891, 'val': 1}
  • id: 111671
    {'lmfdb_iso': '3360.p', 'p': 29, 'prec': 20, 'unit': 1319389720000482748321185456, 'val': 1}
  • id: 111667
    {'lmfdb_iso': '3360.p', 'p': 37, 'prec': 20, 'unit': 484586828396723356657476805555, 'val': 1}
  • id: 111669
    {'lmfdb_iso': '3360.p', 'p': 41, 'prec': 20, 'unit': 3648665938707748791699805402206, 'val': 1}
  • id: 111670
    {'lmfdb_iso': '3360.p', 'p': 43, 'prec': 20, 'unit': 2085231523065302496911094283988, 'val': 1}
  • id: 111681
    {'lmfdb_iso': '3360.p', 'p': 47, 'prec': 20, 'unit': 21312628398845737848147456568364, 'val': 1}
  • id: 111676
    {'lmfdb_iso': '3360.p', 'p': 53, 'prec': 20, 'unit': 254281755932689505405072227734785, 'val': 1}
  • id: 111677
    {'lmfdb_iso': '3360.p', 'p': 59, 'prec': 20, 'unit': 475310208606403911225378682158370, 'val': 1}
  • id: 111682
    {'lmfdb_iso': '3360.p', 'p': 61, 'prec': 20, 'unit': 3744365164917968690457173205707229, 'val': 1}
  • id: 111675
    {'lmfdb_iso': '3360.p', 'p': 67, 'prec': 20, 'unit': 33831189390482367438264913005244413, 'val': 1}
  • id: 111668
    {'lmfdb_iso': '3360.p', 'p': 71, 'prec': 20, 'unit': 127239782348141074223417641046887921, 'val': 1}
  • id: 111678
    {'lmfdb_iso': '3360.p', 'p': 73, 'prec': 20, 'unit': 140526353592863382090633524831421994, 'val': 1}
  • id: 111673
    {'lmfdb_iso': '3360.p', 'p': 79, 'prec': 20, 'unit': 349539706368571649426389808525238012, 'val': 1}
  • id: 111665
    {'lmfdb_iso': '3360.p', 'p': 83, 'prec': 20, 'unit': 1064309234217737918857181017827336800, 'val': 1}
  • id: 111680
    {'lmfdb_iso': '3360.p', 'p': 89, 'prec': 20, 'unit': 4162995191499893041119651850445821439, 'val': 1}
  • id: 111664
    {'lmfdb_iso': '3360.p', 'p': 97, 'prec': 20, 'unit': 42383510998591456460752911942931822873, 'val': 1}