Elliptic curve data - 306.b1

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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': '306c', 'Clabel': '306c5', 'Cnumber': 5, 'abc_quality': 1.0608330168932623, 'absD': 3792258, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 816, 'ainvs': [1, -1, 0, -249696, 48087270], 'analytic_rank': 0, 'bad_primes': [2, 3, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 306, 'degree': 1024, 'elladic_images': ['16.48.0.213'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3963844299755270999354496751', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [2361739090258884097, 5202], 'lmfdb_iso': '306.b', 'lmfdb_label': '306.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -27744, -1781010], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.r.1', '12.12.0-4.c.1.1', '16.48.0.l.2', '24.48.0-8.r.1.6', '48.96.0-16.l.2.3', '136.48.0.?', '272.96.1.?', '408.96.0.?', '816.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 34], [17, 18, 18]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84707828564147225423782705664', 'prec': 103}, 'szpiro_ratio': 8.54317753387332, '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, 0, 1, 2, 0, 0, -1, 0, -2, 4, 0, -2, 0, 0, 1, -1, 0, 4, 2], 'aplist': [-1, 0, 2, 0, 4, -2, -1, 4, 0, 10, 8, -2, -10, 12, 0, -6, -12, -10, -12, 0, 10, -8, -4, 6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 306, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '306.b', 'trace_hash': 1871933457616851804}
• 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': '0.061251382403982695380060598876', 'prec': 107}, 'conductor': 306, 'gens': [], 'heights': [], 'lmfdb_label': '306.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1471740368869128868905159693', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1471740368869128868905159692776117425', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[1155, -1155, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '306.b1'}
• ec_torsion_growth •

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

  
  
  • id: 12877
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [4]}
  • id: 12876
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [4]}
  • id: 12875
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [2, 2]}
  • id: 12880
    {'degree': 4, 'field': [-2, 14, -13, -2, 1], 'lmfdb_label': '306.b1', 'torsion': [8]}
  • id: 12878
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [2, 4]}
  • id: 12879
    {'degree': 4, 'field': [289, 0, -68, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [8]}
  • id: 12883
    {'degree': 8, 'field': [-50, 180, -38, -260, 71, 68, -18, -4, 1], 'lmfdb_label': '306.b1', 'torsion': [2, 8]}
  • id: 12884
    {'degree': 8, 'field': [-6, -85, 70, 33, -23, 5, 3, -4, 1], 'lmfdb_label': '306.b1', 'torsion': [6]}
  • id: 12882
    {'degree': 8, 'field': [4, 0, 0, 0, -2, 0, 0, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [8]}
  • id: 12881
    {'degree': 8, 'field': [334084, 0, 0, 0, 578, 0, 0, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [2, 4]}
  • id: 12886
    {'degree': 16, 'field': [1, 0, -4, 0, 8, 0, -24, 0, 47, 0, -24, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [2, 8]}
  • id: 12891
    {'degree': 16, 'field': [324, 0, -5043, 0, -1958, 0, -1677, 0, -117, 0, 23, 0, 51, 0, -6, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [12]}
  • id: 12892
    {'degree': 16, 'field': [20736, 0, -15576, 0, 4228, 0, -4056, 0, 252, 0, -404, 0, 24, 0, -12, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [12]}
  • id: 12890
    {'degree': 16, 'field': [20736, 0, 12856, 0, 1444, 0, -2616, 0, -1444, 0, -340, 0, -24, 0, 4, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [2, 6]}
  • id: 12887
    {'degree': 16, 'field': [1336336, 0, -10690688, 0, 15171344, 0, -7153328, 0, 1470721, 0, -143344, 0, 6596, 0, -136, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [2, 16]}
  • id: 12888
    {'degree': 16, 'field': [21381376, 0, -10690688, 0, 2672672, 0, -1021904, 0, 250852, 0, -15028, 0, 578, 0, -34, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [16]}
  • id: 12889
    {'degree': 16, 'field': [27060804, 0, 0, 0, -749088, 0, 0, 0, 15534, 0, 0, 0, -144, 0, 0, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [16]}
  • id: 12885
    {'degree': 16, 'field': [6975757441, 0, -1641354692, 0, 193100552, 0, -34076568, 0, 3925487, 0, -117912, 0, 2312, 0, -68, 0, 1], 'lmfdb_label': '306.b1', 'torsion': [4, 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: 2831
    {'conductor': 306, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '306.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2832
    {'conductor': 306, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '306.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2833
    {'conductor': 306, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '306.b1', 'prime': 17, 'reduction_type': -1, '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: 1667030
    {'adelic_gens': [[5, 4, 812, 813], [1, 16, 0, 1], [271, 0, 0, 815], [628, 69, 567, 418], [15, 2, 718, 803], [685, 288, 48, 229], [1, 0, 16, 1], [801, 16, 800, 17], [727, 288, 774, 121]], 'adelic_image': '816.192.1.?', 'conductor': 306, 'lmfdb_label': '306.b1', 'prime': 0}
  • id: 1233
    {'conductor': 306, 'elladic_image': '16.48.0.213', 'lmfdb_label': '306.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 306.b does not appear in ec_padic