Elliptic curve data - 1225.e1

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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': '1225a3', 'Cnumber': 3, 'abc_quality': 1.0211201298201755, 'absD': 25132537841796875, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 630, 'ainvs': [0, 1, 1, -160883, 25929019], 'analytic_rank': 0, 'bad_primes': [5, 7], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 1225, 'degree': 6912, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9051361543757115741607239400', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3, 9], 'jinv': [-250523582464, 13671875], 'lmfdb_iso': '1225.e', 'lmfdb_label': '1225.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -131, -650], 'min_quad_twist_disc': -35, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0-3.a.1.2', '9.12.0.a.1', '18.24.0-9.a.1.2', '63.36.0.e.2', '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': 0, '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': '0.12746212363100473430766790166', 'prec': 103}, 'szpiro_ratio': 6.703847782640383, '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': '0.022142148635171200868294309148', 'prec': 107}, 'conductor': 1225, 'gens': [], 'heights': [], 'lmfdb_label': '1225.e1', '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.e1'}
• ec_torsion_growth •

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

  
  
  • id: 60796
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '1225.e1', 'torsion': [3]}
  • id: 60797
    {'degree': 3, 'field': [-2, 2, 0, 1], 'lmfdb_label': '1225.e1', 'torsion': [2]}
  • id: 60798
    {'degree': 6, 'field': [1, -3, 8, -11, 8, -3, 1], 'lmfdb_label': '1225.e1', 'torsion': [2, 2]}
  • id: 60801
    {'degree': 6, 'field': [4, -52, 28, 13, -5, -3, 1], 'lmfdb_label': '1225.e1', 'torsion': [6]}
  • id: 60799
    {'degree': 6, 'field': [189, 0, 0, -14, 0, 0, 1], 'lmfdb_label': '1225.e1', 'torsion': [3]}
  • id: 60800
    {'degree': 6, 'field': [280, 1260, 756, -35, -63, 0, 1], 'lmfdb_label': '1225.e1', 'torsion': [9]}
  • id: 60802
    {'degree': 12, 'field': [-2, 4, -4, -4, -6, 8, -20, 0, -4, -10, 2, 0, 1], 'lmfdb_label': '1225.e1', 'torsion': [4]}
  • id: 60805
    {'degree': 12, 'field': [1, -3, 1, -2, 23, -43, 50, -43, 23, -2, 1, -3, 1], 'lmfdb_label': '1225.e1', 'torsion': [2, 6]}
  • id: 60803
    {'degree': 12, 'field': [1884, -5184, 5529, -2910, 1752, -2058, 1471, -504, 123, -58, 24, -6, 1], 'lmfdb_label': '1225.e1', 'torsion': [3, 3]}
  • id: 60804
    {'degree': 12, 'field': [12096, 0, 0, -5544, 0, 0, 751, 0, 0, -29, 0, 0, 1], 'lmfdb_label': '1225.e1', 'torsion': [9]}
  • id: 60806
    {'degree': 18, 'field': [42875, 0, 0, 0, 0, 0, 2891, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1225.e1', 'torsion': [2, 6]}
  • id: 60807
    {'degree': 18, 'field': [3315781, -17431260, 37707705, -38642380, 15573915, 1296540, -2826124, 2030070, -1093680, -38808, 88935, 13230, -2331, -210, -315, -14, 0, 0, 1], 'lmfdb_label': '1225.e1', 'torsion': [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: 18055
    {'conductor': 1225, 'conductor_valuation': 2, 'discriminant_valuation': 15, 'j_denominator_valuation': 9, 'kodaira_symbol': -13, 'lmfdb_label': '1225.e1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 18056
    {'conductor': 1225, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1225.e1', '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: 1672277
    {'adelic_gens': [[344, 621, 225, 554], [613, 18, 612, 19], [1, 18, 0, 1], [1, 18, 0, 281], [1, 18, 10, 181], [10, 9, 81, 73], [1, 0, 18, 1], [620, 621, 513, 8]], 'adelic_image': '630.144.3.?', 'conductor': 1225, 'lmfdb_label': '1225.e1', 'prime': 0}
  • id: 5869
    {'conductor': 1225, 'elladic_image': '9.12.0.1', 'lmfdb_label': '1225.e1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 1225.e does not appear in ec_padic