Elliptic curve data - 2700.q2

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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': '2700r', 'Clabel': '2700r1', 'Cnumber': 1, 'abc_quality': 0.6989700043360189, 'absD': 1968300000000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 12, 'ainvs': [0, 0, 0, -3375, 33750], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 2700, 'degree': 3240, 'elladic_images': ['3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0536398074088034939987784740', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 16, 'isogeny_degrees': [1, 3], 'jinv': [2160, 1], 'lmfdb_iso': '2700.q', 'lmfdb_label': '2700.q2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -15, -10], 'min_quad_twist_disc': -15, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '12.16.0-12.b.1.4'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3053761377549758972263164235', 'prec': 103}, 'szpiro_ratio': 4.554616216114989, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, 2, 0, 0, 0, 3, 0, -1, 0, 0, 0, 6, 0, 2, 0], 'aplist': [0, 0, 0, 2, 3, -1, 6, 2, -3, 6, -4, -7, 0, 2, 3, -6, 15, 5, 2, 9, 2, -10, -12, 18, 17], 'class_deg': 3, 'class_size': 2, 'conductor': 2700, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '2700.q', 'trace_hash': 1492140478136098554}
• 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': '0.12156822941840008010664907349', 'prec': 103}, 'conductor': 2700, 'gens': [], 'heights': [], 'lmfdb_label': '2700.q2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.74260518346049006948154449467', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2278155503814702084446334840062582108', 'prec': 130}, 'tamagawa_product': 27, 'torsion_generators': [[75, 450, 1]], 'xcoord_integral_points': [75]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a'}, 'iwp0': 5, 'lmfdb_label': '2700.q2'}
• ec_torsion_growth •

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

  
  
  • id: 139668
    {'degree': 3, 'field': [-20, -15, 0, 1], 'lmfdb_label': '2700.q2', 'torsion': [6]}
  • id: 139669
    {'degree': 6, 'field': [-8, 0, 42, -10, -21, 0, 1], 'lmfdb_label': '2700.q2', 'torsion': [2, 6]}
  • id: 139670
    {'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '2700.q2', 'torsion': [3, 3]}
  • id: 139671
    {'degree': 9, 'field': [-1, -9, -27, -54, -72, -63, -33, -9, 0, 1], 'lmfdb_label': '2700.q2', 'torsion': [9]}
  • id: 139672
    {'degree': 12, 'field': [-8, 48, -156, 340, -522, 576, -456, 252, -84, 4, 12, -6, 1], 'lmfdb_label': '2700.q2', 'torsion': [12]}
  • id: 139673
    {'degree': 18, 'field': [3, -27, 105, -216, 234, -102, 34, -258, 621, -801, 741, -582, 448, -336, 216, -108, 39, -9, 1], 'lmfdb_label': '2700.q2', 'torsion': [3, 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: 47320
    {'conductor': 2700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '2700.q2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 47321
    {'conductor': 2700, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '2700.q2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 47322
    {'conductor': 2700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '2700.q2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1681568
    {'adelic_gens': [[4, 3, 9, 7], [9, 10, 2, 5], [1, 6, 0, 1], [1, 0, 6, 1], [7, 6, 9, 7], [3, 4, 8, 11], [10, 9, 11, 2], [7, 6, 6, 7]], 'adelic_image': '12.16.0.?', 'conductor': 2700, 'lmfdb_label': '2700.q2', 'prime': 0}
  • id: 13456
    {'conductor': 2700, 'elladic_image': '3.8.0.1', 'lmfdb_label': '2700.q2', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 2700.q does not appear in ec_padic