Elliptic curve data - 304704.ez1

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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': '304704ez', 'Clabel': '304704ez1', 'Cnumber': 1, 'abc_quality': 1.0553025164092962, 'absD': 120235330469302753738752, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 6, 'ainvs': [0, 0, 0, -174620784, 888318315488], 'analytic_rank': 0, 'bad_primes': [2, 3, 23], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 304704, 'degree': 62177280, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4260792257929037816209362490', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 129, 'isogeny_degrees': [1], 'jinv': [-1190106112, 243], 'lmfdb_iso': '304704.ez', 'lmfdb_label': '304704.ez1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -9169, -334955], 'min_quad_twist_disc': -552, 'modell_images': [], 'modm_images': ['6.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 4761], [3, 8, 33856], [23, 112, 576]], 'sha': 16, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.54481047580204533406908453767', 'prec': 107}, 'szpiro_ratio': 5.428669980282766, '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, 2, 0, -1, 0, 0, 0, 6, 0, 7, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, 2, -1, 6, 7, 2, 0, 0, 10, 8, 7, 0, 9, 8, -2, 4, 7, 3, 12, -14, 8, -14, 12, 6], 'class_deg': 1, 'class_size': 1, 'conductor': 304704, 'isogeny_matrix': [[1]], 'lmfdb_iso': '304704.ez', 'trace_hash': 2103765741129177033}
• 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': '0.0010571713752685454163585669512', 'prec': 110}, 'conductor': 304704, 'gens': [], 'heights': [], 'lmfdb_label': '304704.ez1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10182047888568756137734062394', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.5165106486840039281497999321500411668', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 304704.ez1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12876774
    {'degree': 3, 'field': [-46, 0, 0, 1], 'lmfdb_label': '304704.ez1', 'torsion': [2]}
  • id: 12876775
    {'degree': 6, 'field': [75, 15, -14, -3, 4, -3, 1], 'lmfdb_label': '304704.ez1', 'torsion': [2, 2]}
  • id: 12876776
    {'degree': 8, 'field': [-2056752, 0, -198720, 0, 4968, 0, 0, 0, 1], 'lmfdb_label': '304704.ez1', 'torsion': [3]}
  • id: 12876777
    {'degree': 12, 'field': [-158700, 0, 67712, 0, -6348, 0, 460, 0, 92, 0, 0, 0, 1], 'lmfdb_label': '304704.ez1', 'torsion': [4]}
• 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: 7545743
    {'conductor': 304704, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '304704.ez1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 7545744
    {'conductor': 304704, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '304704.ez1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7545745
    {'conductor': 304704, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '304704.ez1', 'prime': 23, 'reduction_type': 0, '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

  
  {'adelic_gens': [[5, 2, 5, 3], [1, 1, 5, 0], [1, 2, 0, 1], [5, 2, 4, 3], [1, 0, 2, 1]], 'adelic_image': '6.2.0.?', 'conductor': 304704, 'lmfdb_label': '304704.ez1', 'prime': 0}
• lmfdb_iso 304704.ez does not appear in ec_padic