Elliptic curve data - 2142.h1

Formats: - HTML - YAML - JSON - 2025-09-28T05:21:47.551076

• 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': '2142g', 'Clabel': '2142g5', 'Cnumber': 5, 'abc_quality': 1.0624727966937526, 'absD': 13079013983994352968, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 816, 'ainvs': [1, -1, 0, -123467436, 528082919464], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 2142, 'degree': 245760, 'elladic_images': ['8.48.0.217'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1284351136570726082324297396', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [285531136548675601769470657, 17941034271597192], 'lmfdb_iso': '2142.h', 'lmfdb_label': '2142.h1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -13718604, -19563199515], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0.p.1', '12.12.0-4.c.1.1', '24.96.0-8.p.1.1', '272.96.1.?', '816.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.5779767584903157369850026729', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 119], [7, 8, 306], [17, 18, 126]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5791289693230177625348071211', 'prec': 100}, 'szpiro_ratio': 8.802152532509949, '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, -1, 0, 1, 2, 0, 1, -1, 0, -2, -4, 0, -2, -1, 0, 1, -1, 0, 4, 2], 'aplist': [-1, 0, 2, 1, -4, -2, -1, 4, -8, -6, 0, -2, -10, -4, 0, -6, 4, 6, -12, 8, -6, 0, 12, 6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 2142, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '2142.h', 'trace_hash': 1364658063474110909}
• 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': '0.0019172369320784290059903458027', 'prec': 110}, 'conductor': 2142, 'gens': [[162581, 1117864, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '7.5779767584903157369850026729', 'prec': 100}], 'lmfdb_label': '2142.h1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16932626500501134875493668484', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5663010016198961736159848844544123927', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[25667, -25667, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': 'a', '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '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': '2142.h1'}
• ec_torsion_growth •

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

  
  
  • id: 108620
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [4]}
  • id: 108619
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [8]}
  • id: 108618
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [2, 2]}
  • id: 108621
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [2, 8]}
  • id: 108625
    {'degree': 8, 'field': [448, -544, 16, -89, -1, 61, 7, -1, 1], 'lmfdb_label': '2142.h1', 'torsion': [6]}
  • id: 108624
    {'degree': 8, 'field': [676, 0, -252, 0, 10, 0, 6, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [16]}
  • id: 108623
    {'degree': 8, 'field': [9604, 0, 0, 0, -98, 0, 0, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [8]}
  • id: 108622
    {'degree': 8, 'field': [9604, 0, 0, 0, 98, 0, 0, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [2, 4]}
  • id: 108630
    {'degree': 16, 'field': [-172088, 591920, 2275868, 1279736, -439182, -289996, 199977, 20978, -42959, -16244, 4437, 190, -117, 136, -1, -2, 1], 'lmfdb_label': '2142.h1', 'torsion': [2, 6]}
  • id: 108629
    {'degree': 16, 'field': [1633, -1516, 2812, -3004, 2948, -2848, 2712, -1516, 773, -776, 516, -20, -118, 28, 16, -8, 1], 'lmfdb_label': '2142.h1', 'torsion': [2, 16]}
  • id: 108631
    {'degree': 16, 'field': [1764, 0, -4851, 0, 490, 0, -2301, 0, -741, 0, -41, 0, 51, 0, -6, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [24]}
  • id: 108627
    {'degree': 16, 'field': [153664, 0, 0, 0, 0, 0, 0, 0, 392, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [2, 8]}
  • id: 108632
    {'degree': 16, 'field': [451584, 0, -620928, 0, 31360, 0, -73632, 0, -11856, 0, -328, 0, 204, 0, -12, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [12]}
  • id: 108626
    {'degree': 16, 'field': [5764801, 0, -3294172, 0, 941192, 0, -403368, 0, 112847, 0, -8232, 0, 392, 0, -28, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [4, 8]}
  • id: 108628
    {'degree': 16, 'field': [92236816, 0, -527067520, 0, 438595472, 0, -133111440, 0, 17789009, 0, -1070160, 0, 26852, 0, -280, 0, 1], 'lmfdb_label': '2142.h1', 'torsion': [2, 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: 35565
    {'conductor': 2142, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '2142.h1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 35566
    {'conductor': 2142, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '2142.h1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 35567
    {'conductor': 2142, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2142.h1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 35568
    {'conductor': 2142, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '2142.h1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1677889
    {'adelic_gens': [[5, 4, 812, 813], [76, 345, 411, 682], [1, 16, 0, 1], [271, 0, 0, 815], [15, 2, 718, 803], [241, 288, 24, 673], [727, 288, 798, 25], [1, 0, 16, 1], [801, 16, 800, 17]], 'adelic_image': '816.192.1.?', 'conductor': 2142, 'lmfdb_label': '2142.h1', 'prime': 0}
  • id: 10516
    {'conductor': 2142, 'elladic_image': '8.48.0.217', 'lmfdb_label': '2142.h1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 63259
    {'lmfdb_iso': '2142.h', 'p': 5, 'prec': 20, 'unit': 11893034519871, 'val': 1}
  • id: 63265
    {'lmfdb_iso': '2142.h', 'p': 11, 'prec': 20, 'unit': 18056368733268277421, 'val': 1}
  • id: 63263
    {'lmfdb_iso': '2142.h', 'p': 13, 'prec': 20, 'unit': 88860595354652225837, 'val': 1}
  • id: 63266
    {'lmfdb_iso': '2142.h', 'p': 19, 'prec': 20, 'unit': 1010129612598243884961319, 'val': 1}
  • id: 63269
    {'lmfdb_iso': '2142.h', 'p': 23, 'prec': 20, 'unit': 51222849870899991043653990, 'val': 1}
  • id: 63264
    {'lmfdb_iso': '2142.h', 'p': 29, 'prec': 20, 'unit': 2508739357058489627780961271, 'val': 1}
  • id: 63273
    {'lmfdb_iso': '2142.h', 'p': 37, 'prec': 20, 'unit': 213615074852768279218609729349, 'val': 1}
  • id: 63261
    {'lmfdb_iso': '2142.h', 'p': 41, 'prec': 20, 'unit': 3752457310565908272517084630743, 'val': 1}
  • id: 63262
    {'lmfdb_iso': '2142.h', 'p': 43, 'prec': 20, 'unit': 7763987662378607568391263570448, 'val': 1}
  • id: 63267
    {'lmfdb_iso': '2142.h', 'p': 53, 'prec': 20, 'unit': 52562550190558574482302791268005, 'val': 1}
  • id: 63271
    {'lmfdb_iso': '2142.h', 'p': 59, 'prec': 20, 'unit': 2268533555108393790082967772609171, 'val': 1}
  • id: 63272
    {'lmfdb_iso': '2142.h', 'p': 61, 'prec': 20, 'unit': 3760840245335307669767357621648351, 'val': 1}
  • id: 63258
    {'lmfdb_iso': '2142.h', 'p': 67, 'prec': 20, 'unit': 40303616871569770934244738799004316, 'val': 1}
  • id: 63260
    {'lmfdb_iso': '2142.h', 'p': 71, 'prec': 20, 'unit': 140027995176361771244588493165675396, 'val': 1}
  • id: 63268
    {'lmfdb_iso': '2142.h', 'p': 73, 'prec': 20, 'unit': 96721565481566258030915404018752713, 'val': 1}
  • id: 63257
    {'lmfdb_iso': '2142.h', 'p': 83, 'prec': 20, 'unit': 2826679793645879043172955058300756823, 'val': 1}
  • id: 63270
    {'lmfdb_iso': '2142.h', 'p': 89, 'prec': 20, 'unit': 9386932494557246661969237249627510429, 'val': 1}
  • id: 63256
    {'lmfdb_iso': '2142.h', 'p': 97, 'prec': 20, 'unit': 14846377214031307484284630518508439365, 'val': 1}