Elliptic curve data - 304200.f2

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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': '304200f', 'Clabel': '304200f1', 'Cnumber': 1, 'abc_quality': 0.9673858851013342, 'absD': 4014006945360750000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 0, 0, 177450, -91999375], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 304200, 'degree': 5160960, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2514589877869229435426905465', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [702464, 4563], 'lmfdb_iso': '304200.f', 'lmfdb_label': '304200.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 5, 14], 'min_quad_twist_disc': -195, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '52.6.0.c.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 13, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '6.1153984867861294306608468629', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 38025], [3, 6, 33800], [5, 14, 12168], [13, 98, 1800]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61608985168159889395446616651', 'prec': 107}, 'szpiro_ratio': 3.975919065099311, '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, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 0, -4, -2, 0, -6, -4, 4, 6, -8, -10, -4, 4, 6, 6, -6, -6, 0, 10, -2, 0, 10, 8, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 304200, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '304200.f', 'trace_hash': 1564905068600722786}
• 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': '0.011076628005954104824236686200', 'prec': 107}, 'conductor': 304200, 'gens': [[364, 4563, 1], [6409, 514098, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7674819497727345854102351598', 'prec': 100}, {'__RealLiteral__': 0, 'data': '3.8618846387018768568137948053', 'prec': 100}], 'lmfdb_label': '304200.f2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.12346049500607485998923000712', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.080161989408267011664497902283228073', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[325, 0, 1]], 'xcoord_integral_points': [325, 364, 2200, 3241, 6409, 13000, 72400]}
• lmfdb_label 304200.f2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12857665
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '304200.f2', 'torsion': [2, 2]}
  • id: 12857666
    {'degree': 4, 'field': [-1, -8, 0, -1, 1], 'lmfdb_label': '304200.f2', 'torsion': [4]}
  • id: 12857669
    {'degree': 8, 'field': [-1342419, 261690, 53040, -10998, -702, 390, -64, -2, 1], 'lmfdb_label': '304200.f2', 'torsion': [6]}
  • id: 12857668
    {'degree': 8, 'field': [1, 8, 64, -2, -7, 16, 1, -1, 1], 'lmfdb_label': '304200.f2', 'torsion': [2, 4]}
  • id: 12857667
    {'degree': 8, 'field': [19321, 0, 13246, 0, 2607, 0, 94, 0, 1], 'lmfdb_label': '304200.f2', 'torsion': [2, 4]}
  • id: 12857670
    {'degree': 16, 'field': [-34896, -22416, 67560, 93336, -124460, 8004, 35666, -10710, -2825, -476, 1972, -428, -269, 138, -14, -4, 1], 'lmfdb_label': '304200.f2', 'torsion': [8]}
  • id: 12857671
    {'degree': 16, 'field': [85934989, -282712844, 369983202, -181032306, 106937040, -20235672, 7609162, -699176, 121959, 36954, -8988, 684, 68, -112, 36, -8, 1], 'lmfdb_label': '304200.f2', 'torsion': [2, 6]}
• 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: 7533765
    {'conductor': 304200, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '304200.f2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7533766
    {'conductor': 304200, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '304200.f2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7533767
    {'conductor': 304200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '304200.f2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7533768
    {'conductor': 304200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '304200.f2', 'prime': 13, '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: 3576106
    {'adelic_gens': [[1, 2, 2, 5], [145, 4, 134, 9], [106, 1, 103, 0], [3, 4, 8, 11], [153, 4, 152, 5], [1, 4, 0, 1], [41, 118, 116, 39], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 304200, 'lmfdb_label': '304200.f2', 'prime': 0}
  • id: 1070883
    {'conductor': 304200, 'elladic_image': '2.3.0.1', 'lmfdb_label': '304200.f2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 304200.f does not appear in ec_padic