Elliptic curve data - 451770.q3

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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': '451770q', 'Clabel': '451770q1', 'Cnumber': 1, 'abc_quality': 1.035653777739774, 'absD': 1150612794875440005120000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9768, 'ainvs': [1, 1, 0, -55124182, 148812599764], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 37], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 451770, 'degree': 108380160, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3683759268259175265595137106', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 4], 'jinv': [7220044159551112609, 448454983680000], 'lmfdb_iso': '451770.q', 'lmfdb_label': '451770.q3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -40266, 2921559], 'min_quad_twist_disc': 37, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '66.6.0.a.1', '132.12.0.?', '148.12.0.?', '264.24.0.?', '296.24.0.?', '4884.24.0.?', '9768.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 45177], [3, 4, 150590], [5, 6, 30118], [7, 2, 225885], [11, 12, 41070], [37, 686, 330]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5629169705038053043754658751', 'prec': 100}, 'szpiro_ratio': 4.998791009424264, '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, -1, -1, 1, 1, 1, 4, -1, 1, -1, -1, -1, -2, -4, -1, 1, -2, -1, -4, 1], 'aplist': [-1, -1, 1, 4, -1, -2, -2, -4, 4, -6, 0, 0, -6, 12, -4, -6, 4, -10, -12, -4, 10, -4, 4, -10, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 451770, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '451770.q', 'trace_hash': 531537567711498796}
• 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': '0.0011864948131513879006346098407', 'prec': 110}, 'conductor': 451770, 'gens': [], 'heights': [], 'lmfdb_label': '451770.q3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.085324869411500109091824330180', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.68259895529200087273459464143657987641', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[5084, -2542, 1]], 'xcoord_integral_points': [5084]}
• lmfdb_label 451770.q3 does not appear in ec_iwasawa
• lmfdb_label 451770.q3 does not appear in ec_torsion_growth
• 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: 11149912
    {'conductor': 451770, 'conductor_valuation': 1, 'discriminant_valuation': 28, 'j_denominator_valuation': 28, 'kodaira_symbol': 32, 'lmfdb_label': '451770.q3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 11149913
    {'conductor': 451770, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '451770.q3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 11149914
    {'conductor': 451770, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '451770.q3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 11149915
    {'conductor': 451770, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '451770.q3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 11149916
    {'conductor': 451770, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '451770.q3', 'prime': 37, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 4444969
    {'adelic_gens': [[1, 0, 8, 1], [2480, 7659, 1517, 5810], [1, 8, 0, 1], [1, 4, 4, 17], [9761, 8, 9760, 9], [8104, 7659, 6253, 5810], [371, 6438, 962, 2147], [7697, 3996, 5846, 7031], [7, 6, 9762, 9763], [5807, 0, 0, 9767]], 'adelic_image': '9768.48.0.?', 'conductor': 451770, 'lmfdb_label': '451770.q3', 'prime': 0}
  • id: 1510463
    {'conductor': 451770, 'elladic_image': '8.12.0.11', 'lmfdb_label': '451770.q3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 451770.q does not appear in ec_padic