Elliptic curve data - 49686.u2

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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': '49686k', 'Clabel': '49686k2', 'Cnumber': 2, 'abc_quality': 0.9566415663757943, 'absD': 169290909941454756, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2184, 'ainvs': [1, 1, 0, -223759, -35700335], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 49686, 'degree': 774144, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0328288171289848652691959077', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2], 'jinv': [2181825073, 298116], 'lmfdb_iso': '49686.u', 'lmfdb_label': '49686.u2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -27, 45], 'min_quad_twist_disc': -91, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '24.12.0-2.a.1.2', '52.12.0-2.a.1.1', '56.12.0.a.1', '84.12.0.?', '168.24.0.?', '312.24.0.?', '728.24.0.?', '1092.24.0.?', '2184.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.22260093612944015531022418480', 'prec': 107}, 'szpiro_ratio': 4.491485757494363, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 2, 1, 0, -1, 1, -2, 4, -1, 0, 0, -2, 1, -6, -1, -4, 2], 'aplist': [-1, -1, 2, 0, 4, 0, -6, -4, 0, -6, -8, -10, -6, 4, 4, 10, 4, 6, 8, 0, -10, -8, 4, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 49686, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '49686.u', 'trace_hash': 2099135684412784163}
• 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': '0.017151706014422714917494679433', 'prec': 107}, 'conductor': 49686, 'gens': [], 'heights': [], 'lmfdb_label': '49686.u2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.22149810993199100935915639746', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.88599243972796403743662558985692711743', 'prec': 133}, 'tamagawa_product': 64, 'torsion_generators': [[-190, 95, 1], [538, -269, 1]], 'xcoord_integral_points': [-190, 538]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 1], '3': [0, 0], '7': 'a', '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '49686.u2'}
• ec_torsion_growth •

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

  
  
  • id: 2415600
    {'degree': 4, 'field': [4, 0, 17, 0, 1], 'lmfdb_label': '49686.u2', 'torsion': [2, 4]}
  • id: 2415601
    {'degree': 4, 'field': [303, -22, 23, -2, 1], 'lmfdb_label': '49686.u2', 'torsion': [2, 4]}
  • id: 2415602
    {'degree': 4, 'field': [676, 0, -130, 0, 1], 'lmfdb_label': '49686.u2', 'torsion': [2, 4]}
  • id: 2415603
    {'degree': 8, 'field': [-1862, -175, -2120, -2067, 81, -267, -5, -4, 1], 'lmfdb_label': '49686.u2', 'torsion': [2, 6]}
  • id: 2415604
    {'degree': 16, 'field': [108676, 73496, -79988, -3400, 41018, -41440, 1110, 16244, -8779, 256, 2514, -1004, -136, 112, 4, -8, 1], 'lmfdb_label': '49686.u2', 'torsion': [4, 4]}
  • id: 2415606
    {'degree': 16, 'field': [298841, 54712, 521812, -1055664, 325810, 137768, 95680, -59672, -53493, 32488, 5840, -5752, 170, 336, -28, -8, 1], 'lmfdb_label': '49686.u2', 'torsion': [2, 8]}
  • id: 2415607
    {'degree': 16, 'field': [60168969, 51242184, -36971388, -26179776, 7454994, 6027048, -843552, -884520, 86923, 76264, -3056, -5384, -134, 448, -44, -8, 1], 'lmfdb_label': '49686.u2', 'torsion': [2, 8]}
  • id: 2415605
    {'degree': 16, 'field': [877166689, 0, 344390130, 0, 47844601, 0, 1829646, 0, 259716, 0, 2418, 0, 745, 0, 6, 0, 1], 'lmfdb_label': '49686.u2', 'torsion': [2, 8]}
• 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: 1188364
    {'conductor': 49686, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '49686.u2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1188365
    {'conductor': 49686, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '49686.u2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1188366
    {'conductor': 49686, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '49686.u2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1188367
    {'conductor': 49686, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '49686.u2', '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: 1994817
    {'adelic_gens': [[1, 0, 4, 1], [167, 2180, 334, 2175], [1639, 4, 0, 1], [1, 4, 0, 1], [621, 2182, 314, 1], [1093, 2, 0, 1], [2181, 4, 2180, 5], [1457, 4, 730, 9]], 'adelic_image': '2184.48.0.?', 'conductor': 49686, 'lmfdb_label': '49686.u2', 'prime': 0}
  • id: 213878
    {'conductor': 49686, 'elladic_image': '2.6.0.1', 'lmfdb_label': '49686.u2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 49686.u does not appear in ec_padic