Elliptic curve data - 1225.e2

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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': '1225a', 'Clabel': '1225a1', 'Cnumber': 1, 'abc_quality': 0.8871538351825968, 'absD': 64339296875, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 630, 'ainvs': [0, 1, 1, -1633, -28731], 'analytic_rank': 0, 'bad_primes': [5, 7], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 1225, 'degree': 768, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.80652386570760188276547870305', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3, 9], 'jinv': [-262144, 35], 'lmfdb_iso': '1225.e', 'lmfdb_label': '1225.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -1, 0], 'min_quad_twist_disc': -35, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0-3.a.1.1', '9.12.0.a.1', '18.24.0-9.a.1.1', '63.36.0.e.1', '70.2.0.a.1', '105.8.0.?', '126.72.0.?', '210.16.0.?', '315.72.0.?', '630.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[5, 18, 49], [7, 32, 25]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.97115016503710495708757733528', 'prec': 107}, 'szpiro_ratio': 4.783825748994121, '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, 1, -2, 0, 0, 0, 0, -2, 0, -3, -2, 5, 0, 0, 4, 3, 0, -2, 0], 'aplist': [0, 1, 0, 0, -3, 5, 3, -2, 6, 3, 4, -2, 12, 10, 9, -12, 0, -8, 4, 0, 2, -1, 12, 12, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 1225, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '1225.e', 'trace_hash': 586242828473374160}
• 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': '0.19927933771654080781464878233', 'prec': 103}, 'conductor': 1225, 'gens': [], 'heights': [], 'lmfdb_label': '1225.e2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.37272051036242449721741985684', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4908820414496979888696794273457314143', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': [4, 0], '5': 'a', '7': 'a', '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '1225.e2'}
• ec_torsion_growth •

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

  
  
  • id: 60776
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '1225.e2', 'torsion': [3]}
  • id: 60777
    {'degree': 3, 'field': [-2, 2, 0, 1], 'lmfdb_label': '1225.e2', 'torsion': [2]}
  • id: 60779
    {'degree': 6, 'field': [-6, -33, 25, 15, -5, -3, 1], 'lmfdb_label': '1225.e2', 'torsion': [3]}
  • id: 60778
    {'degree': 6, 'field': [1, -3, 8, -11, 8, -3, 1], 'lmfdb_label': '1225.e2', 'torsion': [2, 6]}
  • id: 60780
    {'degree': 6, 'field': [29, -22, 22, -8, 8, -1, 1], 'lmfdb_label': '1225.e2', 'torsion': [9]}
  • id: 60781
    {'degree': 12, 'field': [-2, 4, -4, -4, -6, 8, -20, 0, -4, -10, 2, 0, 1], 'lmfdb_label': '1225.e2', 'torsion': [4]}
  • id: 60782
    {'degree': 12, 'field': [36, 198, 1239, -645, 1090, 63, 239, 42, 45, -15, 14, -3, 1], 'lmfdb_label': '1225.e2', 'torsion': [3, 3]}
  • id: 60783
    {'degree': 12, 'field': [109, 242, 22, 170, 275, -263, 261, -59, 100, -35, 22, -4, 1], 'lmfdb_label': '1225.e2', 'torsion': [9]}
  • id: 60784
    {'degree': 18, 'field': [1, 0, 0, -76, 0, 0, 505, 0, 0, -230, 0, 0, 85, 0, 0, -6, 0, 0, 1], 'lmfdb_label': '1225.e2', 'torsion': [6]}
  • id: 60785
    {'degree': 18, 'field': [71, -34, 318, -753, 1344, -1960, 2738, -2968, 3166, -2653, 2146, -1414, 876, -448, 210, -79, 26, -6, 1], 'lmfdb_label': '1225.e2', 'torsion': [2, 18]}
• 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: 18051
    {'conductor': 1225, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1225.e2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 18052
    {'conductor': 1225, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1225.e2', 'prime': 7, '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: 1672278
    {'adelic_gens': [[11, 18, 468, 505], [1, 18, 0, 1], [1, 0, 18, 1], [10, 9, 81, 73], [613, 18, 612, 19], [86, 621, 279, 20], [620, 621, 513, 8], [1, 18, 10, 181]], 'adelic_image': '630.144.3.?', 'conductor': 1225, 'lmfdb_label': '1225.e2', 'prime': 0}
  • id: 5870
    {'conductor': 1225, 'elladic_image': '9.12.0.1', 'lmfdb_label': '1225.e2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 1225.e does not appear in ec_padic