Elliptic curve data - 30.a8

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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': '30a', 'Clabel': '30a1', 'Cnumber': 1, 'abc_quality': 0.9968917246282063, 'absD': 2160, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, 1, 2], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 2, 'elladic_images': ['8.12.0.12', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.67828733967764847482561241836', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [357911, 2160], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 1, 2], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.c.1', '6.24.0-6.a.1.4', '8.12.0-4.c.1.2', '12.96.0-12.c.2.7', '20.12.0-4.c.1.2', '24.192.1-24.dh.3.2', '30.48.0-30.b.1.4', '40.24.0-40.bb.1.9', '60.192.1-60.n.4.4', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 15], [3, 4, 10], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.67828733967764847482561241836', 'prec': 107}, 'szpiro_ratio': 4.419554787227392, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
• 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, -4, -1, 1, 1, 0, 1, 2, 4, -1, 1, 6, -1, -4, -1], 'aplist': [-1, 1, -1, -4, 0, 2, 6, -4, 0, -6, 8, 2, -6, -4, 0, -6, 0, -10, -4, 0, 2, 8, 12, 18, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 30, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '30.a', 'trace_hash': 148452494971348580}
• 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': '3.8828704210383193909915001664', 'prec': 100}, 'conductor': 30, 'gens': [], 'heights': [], 'lmfdb_label': '30.a8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.3519482592414964494482281339', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.55865804320691607490803802232401598477', 'prec': 133}, 'tamagawa_product': 6, 'torsion_generators': [[3, 4, 1]], 'xcoord_integral_points': [-1, 0, 3]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 0], '3': [1, 0], '5': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '30.a8'}
• ec_torsion_growth •

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

  
  
  • id: 680
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '30.a8', 'torsion': [12]}
  • id: 681
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '30.a8', 'torsion': [12]}
  • id: 679
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '30.a8', 'torsion': [2, 6]}
  • id: 682
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '30.a8', 'torsion': [2, 12]}
  • id: 683
    {'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '30.a8', 'torsion': [3, 12]}
  • id: 685
    {'degree': 8, 'field': [-4, 16, -10, -16, 19, -16, 10, -4, 1], 'lmfdb_label': '30.a8', 'torsion': [24]}
  • id: 686
    {'degree': 8, 'field': [3, -12, 12, 0, 1, -4, 6, -4, 1], 'lmfdb_label': '30.a8', 'torsion': [24]}
  • id: 684
    {'degree': 8, 'field': [16, 0, -28, 0, 24, 0, -7, 0, 1], 'lmfdb_label': '30.a8', 'torsion': [2, 12]}
  • id: 687
    {'degree': 9, 'field': [16, -48, 0, 44, -24, -24, 11, 0, -3, 1], 'lmfdb_label': '30.a8', 'torsion': [18]}
  • id: 688
    {'degree': 12, 'field': [1, -1, 1, 10, -5, -1, 26, -1, -5, 10, 1, -1, 1], 'lmfdb_label': '30.a8', 'torsion': [6, 12]}
  • id: 690
    {'degree': 16, 'field': [1, -18, 143, -630, 1595, -2292, 2244, -1620, 824, -240, 36, -24, 35, -30, 17, -6, 1], 'lmfdb_label': '30.a8', 'torsion': [2, 24]}
  • id: 689
    {'degree': 16, 'field': [1, -6, 18, -36, 37, 0, -18, 42, -60, 42, -18, 0, 37, -36, 18, -6, 1], 'lmfdb_label': '30.a8', 'torsion': [4, 12]}
  • id: 691
    {'degree': 16, 'field': [36, 0, 54, 0, 75, 18, -63, 30, -44, 42, 25, -78, 72, -42, 19, -6, 1], 'lmfdb_label': '30.a8', 'torsion': [2, 24]}
  • id: 693
    {'degree': 18, 'field': [36, 0, -108, -642, -72, 2646, -2377, 3867, -2505, 806, -948, 516, -276, 120, -33, -19, 12, -3, 1], 'lmfdb_label': '30.a8', 'torsion': [36]}
  • id: 694
    {'degree': 18, 'field': [201, -585, 1539, -3669, 7254, -11286, 14878, -16377, 14961, -11348, 7065, -3627, 1644, -693, 252, -74, 21, -6, 1], 'lmfdb_label': '30.a8', 'torsion': [36]}
  • id: 692
    {'degree': 18, 'field': [2416, -2064, 432, 6236, -9276, -348, 17087, -22572, 15099, -6163, 2373, -1332, 668, -186, 39, -16, 9, -3, 1], 'lmfdb_label': '30.a8', '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: 84
    {'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '30.a8', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 85
    {'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '30.a8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 86
    {'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '30.a8', 'prime': 5, '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: 1665940
    {'adelic_gens': [[1, 12, 12, 25], [112, 21, 75, 106], [97, 24, 96, 25], [1, 0, 24, 1], [97, 24, 102, 7], [1, 24, 0, 1], [9, 28, 20, 29], [16, 63, 41, 74], [15, 106, 14, 11]], 'adelic_image': '120.384.5.?', 'conductor': 30, 'lmfdb_label': '30.a8', 'prime': 0}
  • id: 69
    {'conductor': 30, 'elladic_image': '8.12.0.12', 'lmfdb_label': '30.a8', 'modell_image': '2B', 'prime': 2}
  • id: 70
    {'conductor': 30, 'elladic_image': '3.8.0.1', 'lmfdb_label': '30.a8', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 30.a does not appear in ec_padic