Elliptic curve data - 1470.q1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1470p', 'Clabel': '1470p5', 'Cnumber': 5, 'abc_quality': 1.0369284989490737, 'absD': 370594350, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [1, 0, 0, -823201, 287410955], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 1470, 'degree': 12288, 'elladic_images': ['16.48.0.198'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7097125040017886060141034198', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [524388516989299201, 3150], 'lmfdb_iso': '1470.q', 'lmfdb_label': '1470.q1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -16800, -845133], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.4', '16.48.0-16.e.1.3', '28.12.0-4.c.1.1', '56.48.0-56.bh.1.6', '112.96.0.?', '120.48.0.?', '240.96.0.?', '840.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.73675742947413195346142704808', 'prec': 103}, 'szpiro_ratio': 7.195439864215484, '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, 0, 1, 1, -1, 4, 1, 2, 0, -1, 1, -2, 1, 4, -1], 'aplist': [1, 1, -1, 0, 4, 2, -2, 4, -8, 6, 8, -2, -2, -12, 8, 6, -4, 2, 12, 8, 14, 0, -12, -2, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 1470, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '1470.q', 'trace_hash': 227341795155588699}
• 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': '0.032731249735953704067924543820', 'prec': 107}, 'conductor': 1470, 'gens': [], 'heights': [], 'lmfdb_label': '1470.q1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.82603699755848650488095551389', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3041479902339460195238220555624273127', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[2095, -2095, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [3, 0], '5': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '1470.q1'}
• ec_torsion_growth •

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

  
  
  • id: 73761
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [2, 2]}
  • id: 73762
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [4]}
  • id: 73763
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [4]}
  • id: 73765
    {'degree': 4, 'field': [4, 0, -11, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [8]}
  • id: 73764
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [2, 4]}
  • id: 73766
    {'degree': 4, 'field': [529, 0, -74, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [8]}
  • id: 73771
    {'degree': 8, 'field': [-12, -60, 42, 35, -14, -7, 7, -4, 1], 'lmfdb_label': '1470.q1', 'torsion': [6]}
  • id: 73769
    {'degree': 8, 'field': [196, 0, -420, 0, 197, 0, -30, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [2, 8]}
  • id: 73768
    {'degree': 8, 'field': [226, 248, -196, -112, 77, -28, 14, -4, 1], 'lmfdb_label': '1470.q1', 'torsion': [8]}
  • id: 73770
    {'degree': 8, 'field': [3600, 0, -5400, 0, 1410, 0, -90, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [16]}
  • id: 73767
    {'degree': 8, 'field': [9919366, -63032, 56756, 12544, -6251, -28, 14, -4, 1], 'lmfdb_label': '1470.q1', 'torsion': [2, 4]}
  • id: 73776
    {'degree': 16, 'field': [-27704, 483040, -1589088, -6270688, 20928792, -17759232, -193496, 8122496, -4437450, 645784, 188452, -74304, 4482, 1288, -168, -4, 1], 'lmfdb_label': '1470.q1', 'torsion': [2, 16]}
  • id: 73773
    {'degree': 16, 'field': [2401, 0, 0, 0, 0, 0, 0, 0, 1666, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [2, 8]}
  • id: 73779
    {'degree': 16, 'field': [2744, 3136, -20468, 53592, -67130, 29204, 21217, -24584, 3984, 1126, -91, 140, -175, 42, 14, -8, 1], 'lmfdb_label': '1470.q1', 'torsion': [12]}
  • id: 73778
    {'degree': 16, 'field': [8100, 0, -25272, 0, 12420, 0, 3821, 0, -1858, 0, -415, 0, 85, 0, -14, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [12]}
  • id: 73777
    {'degree': 16, 'field': [16130, -58144, 31800, 57624, -46722, 34236, -24431, -4232, 17940, -7610, -2075, 1884, -223, -70, 30, -8, 1], 'lmfdb_label': '1470.q1', 'torsion': [2, 6]}
  • id: 73775
    {'degree': 16, 'field': [2540160000, 0, 0, 0, -33868800, 0, 0, 0, 213304, 0, 0, 0, -672, 0, 0, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [16]}
  • id: 73772
    {'degree': 16, 'field': [6153500390625, 0, 0, 0, 0, 0, 0, 0, 84341250, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [4, 4]}
  • id: 73774
    {'degree': 16, 'field': [25274750760000, 0, -2987228160000, 0, 142600878000, 0, -2667168000, 0, 27353025, 0, -529200, 0, 10080, 0, 0, 0, 1], 'lmfdb_label': '1470.q1', 'torsion': [16]}
• 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: 22671
    {'conductor': 1470, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1470.q1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 22672
    {'conductor': 1470, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1470.q1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 22673
    {'conductor': 1470, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1470.q1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 22674
    {'conductor': 1470, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1470.q1', 'prime': 7, '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: 1673763
    {'adelic_gens': [[5, 4, 1676, 1677], [1478, 425, 213, 842], [1021, 16, 1088, 1365], [428, 425, 843, 842], [1, 16, 0, 1], [1665, 16, 1664, 17], [1184, 1675, 765, 14], [15, 2, 1582, 1667], [1133, 16, 304, 1365], [1, 0, 16, 1]], 'adelic_image': '1680.192.1.?', 'conductor': 1470, 'lmfdb_label': '1470.q1', 'prime': 0}
  • id: 7134
    {'conductor': 1470, 'elladic_image': '16.48.0.198', 'lmfdb_label': '1470.q1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1470.q does not appear in ec_padic