Elliptic curve data - 2700.r1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '2700o', 'Clabel': '2700o2', 'Cnumber': 2, 'abc_quality': 1.1514167254781673, 'absD': 7593750000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 30, 'ainvs': [0, 0, 0, -1425, 21125], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 2700, 'degree': 2592, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.68220703085898963412326664622', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 3], 'jinv': [-5267712, 125], 'lmfdb_iso': '2700.r', 'lmfdb_label': '2700.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -513, -4563], 'min_quad_twist_disc': -15, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0-3.a.1.2', '15.8.0-3.a.1.2', '30.16.0-30.b.1.1'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3248091943911876574109820908', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 675], [3, 8, 10], [5, 18, 108]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.81131610582308802773087590960', 'prec': 107}, 'szpiro_ratio': 4.232317503580294, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -6, 0, 4, 0, 0, 0, -3, 0, -7, 0], 'aplist': [0, 0, 0, 4, -6, 4, -3, -7, -9, 0, -7, -2, -6, -2, 0, 9, 12, -7, -2, -6, -2, -1, 9, 6, -8], 'class_deg': 3, 'class_size': 2, 'conductor': 2700, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '2700.r', 'trace_hash': 1021452391085916391}
• 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': '0.25553035715030654415175704548', 'prec': 103}, 'conductor': 2700, 'gens': [[20, 25, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3248091943911876574109820908', 'prec': 100}], 'lmfdb_label': '2700.r1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.3172430192798463817226762350', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4901913263790979127337745160068035902', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [20]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '2700.r1'}
• ec_torsion_growth •

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

  
  
  • id: 139636
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '2700.r1', 'torsion': [3]}
  • id: 139637
    {'degree': 3, 'field': [-1, 3, 0, 1], 'lmfdb_label': '2700.r1', 'torsion': [2]}
  • id: 139640
    {'degree': 6, 'field': [-1, 0, 0, -1, 0, 0, 1], 'lmfdb_label': '2700.r1', 'torsion': [6]}
  • id: 139638
    {'degree': 6, 'field': [1, -3, 3, -1, 3, -3, 1], 'lmfdb_label': '2700.r1', 'torsion': [2, 2]}
  • id: 139639
    {'degree': 6, 'field': [96, 0, 0, -18, 0, 0, 1], 'lmfdb_label': '2700.r1', 'torsion': [3]}
  • id: 139641
    {'degree': 12, 'field': [-8, 48, -120, 160, -144, 144, -168, 144, -66, 4, 12, -6, 1], 'lmfdb_label': '2700.r1', 'torsion': [4]}
  • id: 139643
    {'degree': 12, 'field': [1, -6, 24, -61, 111, -153, 164, -138, 93, -50, 21, -6, 1], 'lmfdb_label': '2700.r1', 'torsion': [2, 6]}
  • id: 139642
    {'degree': 12, 'field': [144, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2700.r1', 'torsion': [3, 3]}
  • id: 139644
    {'degree': 18, 'field': [9, -171, 900, 2277, -1035, -3771, 39, 2490, 507, -795, -420, 60, 160, 65, -20, -18, -3, 0, 1], 'lmfdb_label': '2700.r1', 'torsion': [9]}
  • id: 139645
    {'degree': 18, 'field': [1089, -1485, 216, -144, 9207, -30267, 50634, -54945, 41148, -20643, 5706, 387, -1104, 405, 9, -72, 36, -9, 1], 'lmfdb_label': '2700.r1', '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: 47308
    {'conductor': 2700, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '2700.r1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 47309
    {'conductor': 2700, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '2700.r1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 47310
    {'conductor': 2700, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '2700.r1', 'prime': 5, 'reduction_type': 0, '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: 1681569
    {'adelic_gens': [[6, 1, 13, 24], [1, 0, 6, 1], [4, 3, 9, 7], [25, 6, 24, 7], [3, 4, 8, 11], [1, 6, 0, 1], [23, 24, 9, 11]], 'adelic_image': '30.16.0.?', 'conductor': 2700, 'lmfdb_label': '2700.r1', 'prime': 0}
  • id: 13457
    {'conductor': 2700, 'elladic_image': '3.4.0.1', 'lmfdb_label': '2700.r1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 85347
    {'lmfdb_iso': '2700.r', 'p': 7, 'prec': 20, 'unit': 9529923448370033, 'val': 1}
  • id: 85352
    {'lmfdb_iso': '2700.r', 'p': 11, 'prec': 20, 'unit': 760196167280331786, 'val': 1}
  • id: 85350
    {'lmfdb_iso': '2700.r', 'p': 13, 'prec': 20, 'unit': 90565324271954905394, 'val': 1}
  • id: 85353
    {'lmfdb_iso': '2700.r', 'p': 17, 'prec': 20, 'unit': 140743178686913342269868, 'val': 1}
  • id: 85354
    {'lmfdb_iso': '2700.r', 'p': 19, 'prec': 20, 'unit': 336382850329093991293258, 'val': 1}
  • id: 85357
    {'lmfdb_iso': '2700.r', 'p': 23, 'prec': 20, 'unit': 46516747257386940324147665, 'val': 1}
  • id: 85362
    {'lmfdb_iso': '2700.r', 'p': 31, 'prec': 20, 'unit': 11046726417381362007536689115, 'val': 1}
  • id: 85346
    {'lmfdb_iso': '2700.r', 'p': 37, 'prec': 20, 'unit': 459193033568067035899481017498, 'val': 1}
  • id: 85348
    {'lmfdb_iso': '2700.r', 'p': 41, 'prec': 20, 'unit': 2506813775306072263500319640239, 'val': 1}
  • id: 85349
    {'lmfdb_iso': '2700.r', 'p': 43, 'prec': 20, 'unit': 3867942158728172857440520229165, 'val': 1}
  • id: 85355
    {'lmfdb_iso': '2700.r', 'p': 53, 'prec': 20, 'unit': 428439887909070091183401682621671, 'val': 1}
  • id: 85360
    {'lmfdb_iso': '2700.r', 'p': 59, 'prec': 20, 'unit': 870476665373991271188700101309871, 'val': 1}
  • id: 85361
    {'lmfdb_iso': '2700.r', 'p': 61, 'prec': 20, 'unit': 7224535276468883349000423501814777, 'val': 1}
  • id: 85345
    {'lmfdb_iso': '2700.r', 'p': 67, 'prec': 20, 'unit': 38420785747094360975425886282080983, 'val': 1}
  • id: 85359
    {'lmfdb_iso': '2700.r', 'p': 71, 'prec': 20, 'unit': 3582538864931745734522160769412534, 'val': 1}
  • id: 85356
    {'lmfdb_iso': '2700.r', 'p': 73, 'prec': 20, 'unit': 205225537755578874378593378016168650, 'val': 1}
  • id: 85351
    {'lmfdb_iso': '2700.r', 'p': 79, 'prec': 20, 'unit': 564330846897932929197976832439127972, 'val': 1}
  • id: 85344
    {'lmfdb_iso': '2700.r', 'p': 83, 'prec': 20, 'unit': 2061805666253128860314176431148084226, 'val': 1}
  • id: 85358
    {'lmfdb_iso': '2700.r', 'p': 89, 'prec': 20, 'unit': 414164945873743016273539123697294032, 'val': 1}
  • id: 85343
    {'lmfdb_iso': '2700.r', 'p': 97, 'prec': 20, 'unit': 27927981311163006807026204406110255315, 'val': 1}