Elliptic curve data - 276138.bf1

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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': '276138bf', 'Clabel': '276138bf1', 'Cnumber': 1, 'abc_quality': 1.0722866764700134, 'absD': 67045378012242383369926656, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 16008, 'ainvs': [1, -1, 1, -36681224, 403133829707], 'analytic_rank': 1, 'bad_primes': [2, 3, 23, 29], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 276138, 'degree': 156119040, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6374096531319173358081424424', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 31, 'isogeny_degrees': [1, 3], 'jinv': [-50577879066661513, 621261297432576], 'lmfdb_iso': '276138.bf', 'lmfdb_label': '276138.bf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -7705, 1226492], 'min_quad_twist_disc': 69, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '69.8.0-3.a.1.1', '696.8.0.?', '16008.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.3469702037443444171417606006', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 138069], [3, 2, 30682], [11, 2, 138069], [23, 266, 522], [29, 30, 9522]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5203564008332876447071434080', 'prec': 100}, 'szpiro_ratio': 5.345199739803635, '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, 1, 0, 1, -3, 0, -5, 1, 0, -3, 6, 0, -4, -5, 0, 1, 3, 0, 1, -3], 'aplist': [1, 0, -3, -5, 6, -4, 3, 1, 0, 1, -4, 1, 9, 7, 3, -6, -3, 10, 4, -12, 2, -14, 0, -6, -8], 'class_deg': 3, 'class_size': 2, 'conductor': 276138, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '276138.bf', 'trace_hash': 48455149264397617}
• 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': '0.00069276528774613939102219696559', 'prec': 113}, 'conductor': 276138, 'gens': [[-4755, 687961, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.3469702037443444171417606006', 'prec': 100}], 'lmfdb_label': '276138.bf1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.052523657581317659593456355175', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.7349851443190016867226522216158452346', 'prec': 130}, 'tamagawa_product': 44, 'torsion_generators': [], 'xcoord_integral_points': [-4755]}
• lmfdb_label 276138.bf1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11775514
    {'degree': 2, 'field': [-17, -1, 1], 'lmfdb_label': '276138.bf1', 'torsion': [3]}
  • id: 11775515
    {'degree': 3, 'field': [6, -2, -1, 1], 'lmfdb_label': '276138.bf1', 'torsion': [2]}
  • id: 11775518
    {'degree': 6, 'field': [-3699, -819, 894, 27, -56, -1, 1], 'lmfdb_label': '276138.bf1', 'torsion': [6]}
  • id: 11775516
    {'degree': 6, 'field': [696, 0, 49, 0, -14, 0, 1], 'lmfdb_label': '276138.bf1', 'torsion': [2, 2]}
  • id: 11775517
    {'degree': 6, 'field': [7254, 4704, 536, -119, -21, -1, 1], 'lmfdb_label': '276138.bf1', 'torsion': [3]}
  • id: 11775519
    {'degree': 12, 'field': [-365771057364, 220574393964, -34384273878, -2270020080, 838578660, -18128298, -5083459, 15576, 44333, 126, -21, -4, 1], 'lmfdb_label': '276138.bf1', 'torsion': [4]}
  • id: 11775520
    {'degree': 12, 'field': [8649, 116901, 531519, 65364, 50701, 6051, 4346, -3033, 93, 48, -13, -3, 1], 'lmfdb_label': '276138.bf1', 'torsion': [3, 3]}
  • id: 11775521
    {'degree': 12, 'field': [6594129, -1560654, 2934201, -2627154, 1019770, 335778, -84331, -22878, 4758, 630, -115, -6, 1], 'lmfdb_label': '276138.bf1', 'torsion': [2, 6]}
  • id: 11775522
    {'degree': 18, 'field': [-313222092, 335358828, 842525100, 254647686, 56701350, 20511540, 2759641, -2250177, -177819, 160453, -232713, 20169, 1914, -720, -459, 292, -33, -6, 1], 'lmfdb_label': '276138.bf1', 'torsion': [9]}
  • id: 11775523
    {'degree': 18, 'field': [143471088, -79799904, 247317840, -139182876, 172657836, -84144192, 56088864, -20338486, 7936470, -1856045, 532291, -59814, 22814, -1388, 1368, -124, 68, -3, 1], 'lmfdb_label': '276138.bf1', 'torsion': [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: 6842271
    {'conductor': 276138, 'conductor_valuation': 1, 'discriminant_valuation': 11, 'j_denominator_valuation': 11, 'kodaira_symbol': 15, 'lmfdb_label': '276138.bf1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 11}
  • id: 6842272
    {'conductor': 276138, 'conductor_valuation': 2, 'discriminant_valuation': 27, 'j_denominator_valuation': 21, 'kodaira_symbol': -25, 'lmfdb_label': '276138.bf1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6842273
    {'conductor': 276138, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '276138.bf1', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6842274
    {'conductor': 276138, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '276138.bf1', 'prime': 29, '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: 3408012
    {'adelic_gens': [[666, 23, 13685, 6738], [4, 3, 9, 7], [4871, 0, 0, 16007], [12007, 15318, 0, 1], [8005, 15318, 15663, 13939], [1, 6, 0, 1], [3, 4, 8, 11], [16003, 6, 16002, 7], [553, 15318, 9315, 13939], [1, 0, 6, 1]], 'adelic_image': '16008.16.0.?', 'conductor': 276138, 'lmfdb_label': '276138.bf1', 'prime': 0}
  • id: 984441
    {'conductor': 276138, 'elladic_image': '3.4.0.1', 'lmfdb_label': '276138.bf1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 276138.bf does not appear in ec_padic