Elliptic curve data - 672.h1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '672h', 'Clabel': '672h2', 'Cnumber': 2, 'abc_quality': 1.0715559182397578, 'absD': 258048, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 56, 'ainvs': [0, 1, 0, -337, -2497], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 672, 'degree': 128, 'elladic_images': ['8.24.0.60'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.098946783116383823506340944482', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 2, 'intrinsic_torsion': 2, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2, 4], 'jinv': [1036433728, 63], 'lmfdb_iso': '672.h', 'lmfdb_label': '672.h1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -337, 2497], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.p.1.3', '28.24.0-28.h.1.1', '56.48.0-56.br.1.2'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 7], [3, 4, 224], [7, 8, 96]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.59420039744356148591089117698', 'prec': 107}, 'szpiro_ratio': 4.466307816891492, '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, 0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, -4, 0], 'aplist': [0, 1, 2, 1, 0, 2, 2, -4, 0, 6, 0, 6, -6, -8, -8, 6, 12, 10, -16, 8, -6, -8, 12, -14, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 672, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '672.h', 'trace_hash': 1008207659774182763}
• 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': '0.82045717283862425651706564065', 'prec': 103}, 'conductor': 672, 'gens': [], 'heights': [], 'lmfdb_label': '672.h1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1140029072146034680143422097', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2280058144292069360286844194131506895', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-11, 0, 1]], 'xcoord_integral_points': [-11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '672.h1'}
• ec_torsion_growth •

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

  
  
  • id: 31143
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [2, 2]}
  • id: 31145
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [4]}
  • id: 31144
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '672.h1', 'torsion': [4]}
  • id: 31147
    {'degree': 4, 'field': [-63, 0, 0, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [2, 4]}
  • id: 31146
    {'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [2, 4]}
  • id: 31151
    {'degree': 8, 'field': [-48, 0, 512, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [6]}
  • id: 31149
    {'degree': 8, 'field': [196, 0, 196, 0, 35, 0, -14, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [8]}
  • id: 31150
    {'degree': 8, 'field': [1042, 672, 460, 16, 38, -16, 0, -4, 1], 'lmfdb_label': '672.h1', 'torsion': [8]}
  • id: 31148
    {'degree': 8, 'field': [3844, 0, 760, 0, -120, 0, 4, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [4, 4]}
  • id: 31157
    {'degree': 16, 'field': [9, 0, 0, 0, 4060, 0, 0, 0, 30, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [12]}
  • id: 31153
    {'degree': 16, 'field': [324, -3024, 11880, -24672, 27848, -20816, 19700, -11960, 6981, -3804, 1976, -668, 344, -84, 28, -4, 1], 'lmfdb_label': '672.h1', 'torsion': [2, 8]}
  • id: 31154
    {'degree': 16, 'field': [3777, -21096, -45936, 135240, 575260, 921256, 825776, 419064, 84610, -26440, -18032, -1624, 868, 168, -16, -8, 1], 'lmfdb_label': '672.h1', 'torsion': [2, 8]}
  • id: 31155
    {'degree': 16, 'field': [17613, -40320, 23988, -13356, 29376, -20144, -676, -1412, 13574, -14192, 6500, -1036, -320, 176, -20, -4, 1], 'lmfdb_label': '672.h1', 'torsion': [2, 6]}
  • id: 31152
    {'degree': 16, 'field': [20164, 51120, 67128, 53312, 23688, 880, -5788, -6136, -2379, 196, 732, -20, -16, -4, 8, -4, 1], 'lmfdb_label': '672.h1', 'torsion': [2, 8]}
  • id: 31156
    {'degree': 16, 'field': [304704, 0, -12864, 0, 4048, 0, 31872, 0, 7221, 0, 352, 0, 78, 0, 0, 0, 1], 'lmfdb_label': '672.h1', 'torsion': [12]}
• 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: 8257
    {'conductor': 672, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '672.h1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8258
    {'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '672.h1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8259
    {'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '672.h1', 'prime': 7, '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: 1668968
    {'adelic_gens': [[43, 38, 26, 51], [24, 1, 49, 40], [49, 8, 48, 9], [24, 3, 29, 2], [1, 0, 8, 1], [1, 4, 4, 17], [7, 6, 50, 51], [1, 8, 0, 1]], 'adelic_image': '56.48.0.?', 'conductor': 672, 'lmfdb_label': '672.h1', 'prime': 0}
  • id: 3062
    {'conductor': 672, 'elladic_image': '8.24.0.60', 'lmfdb_label': '672.h1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 672.h does not appear in ec_padic