Elliptic curve data - 155682.v3

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '155682i', 'Clabel': '155682i1', 'Cnumber': 1, 'abc_quality': 1.1780968639246816, 'absD': 575102385288, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 15624, 'ainvs': [1, -1, 1, -4505, -120831], 'analytic_rank': 1, 'bad_primes': [2, 3, 31], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 155682, 'degree': 181440, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0134066065925566522427460413', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-140625, 8], 'lmfdb_iso': '155682.v', 'lmfdb_label': '155682.v3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -42, -100], 'min_quad_twist_disc': 93, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '21.64.1.a.3', '24.8.0.a.1', '56.16.0.a.1', '63.192.5.e.4', '93.8.0.?', '168.128.5.?', '217.16.0.?', '504.384.21.?', '651.128.1.?', '744.16.0.?', '1736.32.0.?', '1953.384.5.?', '5208.256.5.?', '15624.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.9090629352841332115952835341', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0697910918727197011869178666', 'prec': 103}, 'szpiro_ratio': 3.0902741822875464, '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, 0, 0, 2, 1, 0, 0, 3, 0, -2, 2, 0, 1, 3, 0, -1, 0], 'aplist': [1, 0, 0, 2, 3, -2, 3, -1, 6, -6, 0, 4, 9, 1, -6, -12, 3, -8, 5, -12, -11, 4, -12, -6, 5], 'class_deg': 21, 'class_size': 4, 'conductor': 155682, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '155682.v', 'trace_hash': 56414263001035032}
• 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': '0.13175472706077810514779843746', 'prec': 103}, 'conductor': 155682, 'gens': [[74433, 19082807, 16]], 'heights': [{'__RealLiteral__': 0, 'data': '7.9090629352841332115952835341', 'prec': 100}], 'lmfdb_label': '155682.v3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.29041675315343739198763620428', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '13.781546268908478537522242007616704063', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 155682.v3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 6981610
    {'degree': 2, 'field': [8, -1, 1], 'lmfdb_label': '155682.v3', 'torsion': [3]}
  • id: 6981611
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '155682.v3', 'torsion': [2]}
  • id: 6981613
    {'degree': 6, 'field': [-1029, 0, 0, -72, 0, 0, 1], 'lmfdb_label': '155682.v3', 'torsion': [3]}
  • id: 6981612
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '155682.v3', 'torsion': [2, 2]}
  • id: 6981614
    {'degree': 6, 'field': [971, -249, 213, -35, 21, -3, 1], 'lmfdb_label': '155682.v3', 'torsion': [21]}
  • id: 6981615
    {'degree': 6, 'field': [1304, -708, 186, -17, 21, -3, 1], 'lmfdb_label': '155682.v3', 'torsion': [6]}
  • id: 6981616
    {'degree': 12, 'field': [-91406584, 200952960, 27270948, -10737416, 11991846, -1563120, 522597, -31746, 8067, -284, 105, -6, 1], 'lmfdb_label': '155682.v3', 'torsion': [4]}
  • id: 6981617
    {'degree': 12, 'field': [260668, -201666, 262413, -131740, 92445, -34626, 16247, -4326, 1455, -260, 63, -6, 1], 'lmfdb_label': '155682.v3', 'torsion': [3, 3]}
  • id: 6981618
    {'degree': 12, 'field': [881504, -391872, 463116, -151520, 99060, -30012, 13533, -3246, 1095, -200, 51, -6, 1], 'lmfdb_label': '155682.v3', 'torsion': [2, 6]}
  • id: 6981620
    {'degree': 18, 'field': [-10084927536, -6923006496, -1352606580, 16512984, 67255920, 37733364, 5648841, -2679804, -817965, -100812, 13014, 12780, 7155, -324, -162, -60, -9, 0, 1], 'lmfdb_label': '155682.v3', 'torsion': [6]}
  • id: 6981621
    {'degree': 18, 'field': [273669031, -50662563, 228798114, -49312232, 94292529, -20310573, 23899702, -4752135, 4036572, -705529, 470022, -69195, 37812, -4431, 2031, -170, 66, -3, 1], 'lmfdb_label': '155682.v3', 'torsion': [42]}
  • id: 6981619
    {'degree': 18, 'field': [841008176, -529108992, 689114448, -349221396, 254998872, -108842688, 57656760, -20928510, 8737956, -2694371, 919071, -238158, 66798, -14112, 3204, -516, 90, -9, 1], 'lmfdb_label': '155682.v3', 'torsion': [9]}
• 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: 3851504
    {'conductor': 155682, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '155682.v3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 3851505
    {'conductor': 155682, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '155682.v3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3851506
    {'conductor': 155682, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '155682.v3', 'prime': 31, '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: 2672318
    {'adelic_gens': [[1, 5208, 0, 1], [10417, 5208, 10416, 5209], [1, 2232, 0, 1], [4713, 11098, 3472, 5457], [1, 0, 13020, 1], [1303, 9114, 3255, 14323], [13609, 2016, 13608, 13609], [4558, 9393, 9765, 5209], [1, 9114, 0, 11161], [1, 930, 9114, 7813], [13889, 6944, 8680, 6945], [6511, 9858, 13020, 1303], [1, 0, 5208, 1], [1, 0, 2016, 1], [1, 0, 6510, 1], [11591, 0, 0, 15623], [2605, 9114, 9765, 9115]], 'adelic_image': '15624.768.21.?', 'conductor': 155682, 'lmfdb_label': '155682.v3', 'prime': 0}
  • id: 595163
    {'conductor': 155682, 'elladic_image': '8.2.0.1', 'lmfdb_label': '155682.v3', 'modell_image': '2G', 'prime': 2}
  • id: 595164
    {'conductor': 155682, 'elladic_image': '3.4.0.1', 'lmfdb_label': '155682.v3', 'modell_image': '3B', 'prime': 3}
  • id: 595165
    {'conductor': 155682, 'elladic_image': '7.8.0.1', 'lmfdb_label': '155682.v3', 'modell_image': '7B', 'prime': 7}
• lmfdb_iso 155682.v does not appear in ec_padic