Elliptic curve data - 27720.t1

Formats: - HTML - YAML - JSON - 2025-03-10T16:33:15.952001

• 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': '27720j', 'Clabel': '27720j4', 'Cnumber': 4, 'abc_quality': 0.9590385905383163, 'absD': 574801920, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9240, 'ainvs': [0, 0, 0, -147843, -21880098], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 27720, 'degree': 65536, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3740432050553592435913103192', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4], 'jinv': [239369344910082, 385], 'lmfdb_iso': '27720.t', 'lmfdb_label': '27720.t1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -16427, 810374], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '56.12.0.y.1', '168.24.0.?', '440.12.0.?', '660.12.0.?', '1320.24.0.?', '3080.24.0.?', '9240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3465], [3, 6, 3080], [5, 6, 5544], [7, 8, 3960], [11, 12, 2520]], 'sha': 16, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.18935214520802119759455825607', 'prec': 103}, 'szpiro_ratio': 4.626172087385563, '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, -1, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, -1, 1, 1, -2, -2, 0, 4, -2, 8, 2, -6, 12, 0, -10, 4, -2, 12, -8, -6, 4, 12, -2, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 27720, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '27720.t', 'trace_hash': 15622065336258647}
• 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': '0.064050310036612023751230409670', 'prec': 107}, 'conductor': 27720, 'gens': [], 'heights': [], 'lmfdb_label': '27720.t1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24347219049837295878533373130', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9477775239869836702826698504096372076', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[-222, 0, 1]], 'xcoord_integral_points': [-222]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': [1, 0], '11': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '27720.t1'}
• ec_torsion_growth •

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

  
  
  • id: 1386457
    {'degree': 2, 'field': [-770, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [2, 2]}
  • id: 1386459
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [4]}
  • id: 1386458
    {'degree': 2, 'field': [165, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [4]}
  • id: 1386460
    {'degree': 4, 'field': [41209, 0, -364, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [2, 4]}
  • id: 1386464
    {'degree': 8, 'field': [-10976, -1568, -3920, -1568, 112, 112, -56, -2, 1], 'lmfdb_label': '27720.t1', 'torsion': [6]}
  • id: 1386462
    {'degree': 8, 'field': [592900, 0, 169400, 0, 13805, 0, 220, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [8]}
  • id: 1386463
    {'degree': 8, 'field': [9486400, 0, 344960, 0, 9464, 0, 112, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [8]}
  • id: 1386461
    {'degree': 8, 'field': [673455721, 14024804, -14070158, 90872, -45845, 488, -158, -4, 1], 'lmfdb_label': '27720.t1', 'torsion': [2, 4]}
  • id: 1386467
    {'degree': 16, 'field': [9653956, 23090496, -10415952, -35217032, 88126288, -59614912, 35326656, -18545636, 6488253, -2005708, 619824, -82684, 22238, -1476, 272, -8, 1], 'lmfdb_label': '27720.t1', 'torsion': [2, 8]}
  • id: 1386470
    {'degree': 16, 'field': [5694211600, 0, 5249963488, 0, 777315616, 0, -4016432, 0, 7808248, 0, -70616, 0, 2716, 0, 28, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [12]}
  • id: 1386469
    {'degree': 16, 'field': [90064748701, -19048360564, 28426415004, -10257688604, -1323240856, 1287847164, 414770524, -32103052, -12003558, 2634788, 104692, -90708, 2912, 1108, -108, -4, 1], 'lmfdb_label': '27720.t1', 'torsion': [12]}
  • id: 1386466
    {'degree': 16, 'field': [108554434576, 0, 25055990848, 0, 3836754096, 0, 338587648, 0, 21798924, 0, 840448, 0, 22316, 0, 168, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [2, 8]}
  • id: 1386465
    {'degree': 16, 'field': [1773009638908641, 0, 0, 0, 4124908337004, 0, 0, 0, -89643834, 0, 0, 0, 29484, 0, 0, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [4, 4]}
  • id: 1386468
    {'degree': 16, 'field': [89294348626560000, 0, -3384333912960000, 0, 83840461689600, 0, -949228156800, 0, 4610390400, 0, -7872480, 0, -18480, 0, 0, 0, 1], 'lmfdb_label': '27720.t1', 'torsion': [2, 6]}
• 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: 639925
    {'conductor': 27720, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '27720.t1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 639926
    {'conductor': 27720, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '27720.t1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 639927
    {'conductor': 27720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27720.t1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 639928
    {'conductor': 27720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27720.t1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 639929
    {'conductor': 27720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27720.t1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1848879
    {'adelic_gens': [[4936, 3, 6165, 3082], [4768, 3, 285, 3082], [9233, 8, 9232, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [5008, 393, 4227, 7294], [3079, 0, 0, 9239], [7, 6, 9234, 9235], [2644, 3081, 7503, 6166], [4243, 4236, 7362, 2701]], 'adelic_image': '9240.48.0.?', 'conductor': 27720, 'lmfdb_label': '27720.t1', 'prime': 0}
  • id: 125329
    {'conductor': 27720, 'elladic_image': '4.6.0.1', 'lmfdb_label': '27720.t1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 27720.t does not appear in ec_padic