Elliptic curve data - 576.e1

Formats: - HTML - YAML - JSON - 2025-09-22T13:32:01.680708

• 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': '576a', 'Clabel': '576a4', 'Cnumber': 4, 'abc_quality': 1.027195810121916, 'absD': 322486272, 'ainvs': [0, 0, 0, -540, -4752], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 6, 'class_size': 4, 'cm': -12, 'conductor': 576, 'degree': 192, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.42703802881963809944620756045', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [54000, 1], 'lmfdb_iso': '576.e', 'lmfdb_label': '576.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -15, 22], 'min_quad_twist_disc': -24, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.97985201631446528478023030577', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 2, 64]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2055928983347136967536638423', 'prec': 103}, 'szpiro_ratio': 4.7966950968952995, '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, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -8, 0], 'aplist': [0, 0, 0, -4, 0, -2, 0, -8, 0, 0, -4, 10, 0, -8, 0, 0, 0, -14, 16, 0, -10, -4, 0, 0, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 576, 'isogeny_matrix': [[1, 3, 2, 6], [3, 1, 6, 2], [2, 6, 1, 3], [6, 2, 3, 1]], 'lmfdb_iso': '576.e', 'trace_hash': 721032213985341556}
• 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': '0.42567630981937971126018287548', 'prec': 103}, 'conductor': 576, 'gens': [[-14, 8, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.97985201631446528478023030577', 'prec': 103}], 'lmfdb_label': '576.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.99149247513405852048982851676', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9430318018414541502288458147999701656', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-12, 0, 1]], 'xcoord_integral_points': [-14, -12, 37, 42]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [3, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 3, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '576.e1'}
• ec_torsion_growth •

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

  
  
  • id: 26104
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [2, 2]}
  • id: 26105
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [6]}
  • id: 26107
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [2, 6]}
  • id: 26106
    {'degree': 4, 'field': [12, 0, -6, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [4]}
  • id: 26108
    {'degree': 6, 'field': [-2, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [6]}
  • id: 26109
    {'degree': 8, 'field': [-2, 16, -16, 4, -8, 8, 2, -4, 1], 'lmfdb_label': '576.e1', 'torsion': [2, 4]}
  • id: 26111
    {'degree': 8, 'field': [1, 0, 4, 0, 3, 0, -2, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [12]}
  • id: 26110
    {'degree': 8, 'field': [9, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [2, 4]}
  • id: 26114
    {'degree': 12, 'field': [1, 0, -12, 0, 39, 0, -52, 0, 27, 0, 0, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [2, 6]}
  • id: 26112
    {'degree': 12, 'field': [4, 0, 24, 0, 60, 0, 44, 0, 0, 0, -6, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [3, 6]}
  • id: 26113
    {'degree': 12, 'field': [756, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [14]}
  • id: 26115
    {'degree': 16, 'field': [1, -12, 68, -232, 488, -564, 194, 396, -665, 444, -62, -152, 162, -92, 34, -8, 1], 'lmfdb_label': '576.e1', 'torsion': [4, 12]}
  • id: 26116
    {'degree': 16, 'field': [4, -32, 112, -256, 500, -824, 1208, -1528, 1654, -1504, 1136, -704, 350, -136, 40, -8, 1], 'lmfdb_label': '576.e1', 'torsion': [2, 8]}
  • id: 26117
    {'degree': 18, 'field': [24, 0, 144, 0, 360, 0, 516, 0, 432, 0, 180, 0, 12, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '576.e1', 'torsion': [18]}
• 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: 6726
    {'conductor': 576, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '576.e1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6727
    {'conductor': 576, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '576.e1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• lmfdb_label 576.e1 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 9486
    {'lmfdb_iso': '576.e', 'p': 7, 'prec': 20, 'unit': 1684163129378391, 'val': 1}
  • id: 9489
    {'lmfdb_iso': '576.e', 'p': 13, 'prec': 20, 'unit': 4207096007372994409, 'val': 2}
  • id: 9491
    {'lmfdb_iso': '576.e', 'p': 19, 'prec': 20, 'unit': 471332063086521365021432, 'val': 1}
  • id: 9493
    {'lmfdb_iso': '576.e', 'p': 31, 'prec': 20, 'unit': 13671801453416964333869421585, 'val': 1}
  • id: 9485
    {'lmfdb_iso': '576.e', 'p': 37, 'prec': 20, 'unit': 79222660934107682781824901855, 'val': 1}
  • id: 9488
    {'lmfdb_iso': '576.e', 'p': 43, 'prec': 20, 'unit': 5718038035707559644863090974153, 'val': 1}
  • id: 9492
    {'lmfdb_iso': '576.e', 'p': 61, 'prec': 20, 'unit': 6114641527379659997703842876622370, 'val': 1}
  • id: 9484
    {'lmfdb_iso': '576.e', 'p': 67, 'prec': 20, 'unit': 25787741241352085751051151389041358, 'val': 1}
  • id: 9487
    {'lmfdb_iso': '576.e', 'p': 73, 'prec': 20, 'unit': 939130079224087283781509618256133, 'val': 2}
  • id: 9490
    {'lmfdb_iso': '576.e', 'p': 79, 'prec': 20, 'unit': 466087272395005289977693072093155562, 'val': 1}
  • id: 9483
    {'lmfdb_iso': '576.e', 'p': 97, 'prec': 20, 'unit': 28534728437224133224295341855784907352, 'val': 1}