Elliptic curve data - 81120.w1

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '81120bh', 'Clabel': '81120bh4', 'Cnumber': 4, 'abc_quality': 1.1653240287550397, 'absD': 59371622729602560000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, -1, 0, -4330767185, 109698599964225], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 81120, 'degree': 36126720, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8531875382048851733515756066', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 22, 'isogeny_degrees': [1, 2, 4], 'jinv': [454357982636417669333824, 3003024375], 'lmfdb_iso': '81120.w', 'lmfdb_label': '81120.w1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -25625841, 49938972705], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '120.24.0.?', '156.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '16.541646680547788280971910794', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 507], [3, 4, 27040], [5, 6, 16224], [7, 2, 27040], [13, 98, 480]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8775656789141714959075997644', 'prec': 100}, 'szpiro_ratio': 6.916384870312774, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, 0, 1, 0, 4, 0, 0, 0, -1, 0, -2, 0, -4, 0], 'aplist': [0, -1, 1, 0, 4, 0, -2, -4, 8, -6, 0, 10, -6, -4, 0, 6, -12, -10, 12, 12, 10, 8, -16, -14, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 81120, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '81120.w', 'trace_hash': 1857490117102346454}
• 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': '0.00044994955728295987144803246855', 'prec': 113}, 'conductor': 81120, 'gens': [[196753285, 2631934631620, 31]], 'heights': [{'__RealLiteral__': 0, 'data': '16.541646680547788280971910794', 'prec': 100}], 'lmfdb_label': '81120.w1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.096708684298653520665998381340', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.3988835464358640900881525845690996832', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[38125, 43940, 1]], 'xcoord_integral_points': [37995, 38125]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [4, 0], '7': [1, 3, 0], '11': [3, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '81120.w1'}
• ec_torsion_growth •

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

  
  
  • id: 3814356
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '81120.w1', 'torsion': [2, 4]}
  • id: 3814357
    {'degree': 4, 'field': [351, 0, -78, 0, 1], 'lmfdb_label': '81120.w1', 'torsion': [8]}
  • id: 3814361
    {'degree': 8, 'field': [-2370, -25020, 22540, -3456, 516, -228, 18, 0, 1], 'lmfdb_label': '81120.w1', 'torsion': [12]}
  • id: 3814359
    {'degree': 8, 'field': [61330, -26680, -41084, 656, 4690, 200, -140, -4, 1], 'lmfdb_label': '81120.w1', 'torsion': [2, 8]}
  • id: 3814358
    {'degree': 8, 'field': [122500, 0, 4216, 0, -696, 0, 4, 0, 1], 'lmfdb_label': '81120.w1', 'torsion': [4, 4]}
  • id: 3814360
    {'degree': 8, 'field': [182914, -41008, 14860, -6448, -26, 200, 16, -4, 1], 'lmfdb_label': '81120.w1', 'torsion': [2, 8]}
  • id: 3814363
    {'degree': 16, 'field': [251519265, -141478560, -9781710, 6757584, -8679902, 7416096, -294714, -1032872, 397143, 30024, -54138, 840, 3156, -20, -84, 0, 1], 'lmfdb_label': '81120.w1', 'torsion': [2, 12]}
  • id: 3814362
    {'degree': 16, 'field': [6194244902976, 0, -7440787291392, 0, 2189810907648, 0, -45888545664, 0, -416248560, 0, -5919264, 0, -19552, 0, 208, 0, 1], 'lmfdb_label': '81120.w1', 'torsion': [16]}
• 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: 1973902
    {'conductor': 81120, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '81120.w1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1973903
    {'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '81120.w1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1973904
    {'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '81120.w1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1973905
    {'conductor': 81120, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '81120.w1', 'prime': 13, '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: 2198739
    {'adelic_gens': [[203, 198, 1370, 587], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [937, 8, 628, 33], [7, 6, 1554, 1555], [1553, 8, 1552, 9], [356, 1559, 97, 1554], [976, 203, 979, 1008], [1048, 3, 1045, 2]], 'adelic_image': '1560.48.0.?', 'conductor': 81120, 'lmfdb_label': '81120.w1', 'prime': 0}
  • id: 332712
    {'conductor': 81120, 'elladic_image': '4.12.0.7', 'lmfdb_label': '81120.w1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4180232
    {'lmfdb_iso': '81120.w', 'p': 11, 'prec': 20, 'unit': 5410671947518393832, 'val': 2}
  • id: 4180233
    {'lmfdb_iso': '81120.w', 'p': 17, 'prec': 20, 'unit': 81302435274732489326290, 'val': 1}
  • id: 4180234
    {'lmfdb_iso': '81120.w', 'p': 19, 'prec': 20, 'unit': 1914703662036699406839111, 'val': 1}
  • id: 4180237
    {'lmfdb_iso': '81120.w', 'p': 23, 'prec': 20, 'unit': 11474032815967678251026547, 'val': 1}
  • id: 4180230
    {'lmfdb_iso': '81120.w', 'p': 29, 'prec': 20, 'unit': 311739144629395049607012779, 'val': 1}
  • id: 4180226
    {'lmfdb_iso': '81120.w', 'p': 37, 'prec': 20, 'unit': 572039578924318660956958743760, 'val': 1}
  • id: 4180228
    {'lmfdb_iso': '81120.w', 'p': 41, 'prec': 20, 'unit': 151248639570363881265579582562, 'val': 1}
  • id: 4180229
    {'lmfdb_iso': '81120.w', 'p': 43, 'prec': 20, 'unit': 7278002535468046430368800011258, 'val': 1}
  • id: 4180235
    {'lmfdb_iso': '81120.w', 'p': 53, 'prec': 20, 'unit': 438439627563153001630125754631920, 'val': 1}
  • id: 4180239
    {'lmfdb_iso': '81120.w', 'p': 59, 'prec': 20, 'unit': 473382558010483999469648162487589, 'val': 1}
  • id: 4180240
    {'lmfdb_iso': '81120.w', 'p': 61, 'prec': 20, 'unit': 3854689206921495925181073746624410, 'val': 1}
  • id: 4180225
    {'lmfdb_iso': '81120.w', 'p': 67, 'prec': 20, 'unit': 1470488431869226050867015541859004, 'val': 1}
  • id: 4180227
    {'lmfdb_iso': '81120.w', 'p': 71, 'prec': 20, 'unit': 57170962853835268888749292752971096, 'val': 1}
  • id: 4180236
    {'lmfdb_iso': '81120.w', 'p': 73, 'prec': 20, 'unit': 19759719412476007789463459731183791, 'val': 1}
  • id: 4180231
    {'lmfdb_iso': '81120.w', 'p': 79, 'prec': 20, 'unit': 485742530406963238800182249864097926, 'val': 1}
  • id: 4180224
    {'lmfdb_iso': '81120.w', 'p': 83, 'prec': 20, 'unit': 2422545726473922417847897274077577521, 'val': 1}
  • id: 4180238
    {'lmfdb_iso': '81120.w', 'p': 89, 'prec': 20, 'unit': 3914356522047132677601360511809986037, 'val': 1}
  • id: 4180223
    {'lmfdb_iso': '81120.w', 'p': 97, 'prec': 20, 'unit': 41260088309032038227435110863238001830, 'val': 1}