Elliptic curve data - 77315.e2

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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': '77315c', 'Clabel': '77315c1', 'Cnumber': 1, 'abc_quality': 0.9184915288185983, 'absD': 127183175, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1316, 'ainvs': [1, -1, 0, -85, -600], 'analytic_rank': 1, 'bad_primes': [5, 7, 47], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 77315, 'degree': 22656, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.24503723132100736212873828905', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [-658503, 1225], 'lmfdb_iso': '77315.e', 'lmfdb_label': '77315.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -85, -600], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.d.1', '94.6.0.?', '1316.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.5976152441937339027141879585', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.71749966910650728457649937839', 'prec': 107}, 'szpiro_ratio': 2.3443096651600763, '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, -1, 0, 1, -3, -3, -1, -6, 0, 2, 1, 0, -1, -2, -3, -8, 1], 'aplist': [1, 0, -1, 1, -6, 2, -2, -8, -2, 0, -4, 2, -6, -10, 0, 6, 8, 10, 10, 0, -14, 16, 12, 14, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 77315, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '77315.e', 'trace_hash': 479613262221259233}
• 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': '0.61258077810290519452724065715', 'prec': 103}, 'conductor': 77315, 'gens': [[200, 2720, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.5976152441937339027141879585', 'prec': 100}], 'lmfdb_label': '77315.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.74028156777562025339919775039', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8459333708991759580348948950396947771', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[12, -6, 1]], 'xcoord_integral_points': [12, 200]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': [1, 1, 0], '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': 'a'}, 'iwp0': 0, 'lmfdb_label': '77315.e2'}
• ec_torsion_growth •

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

  
  
  • id: 3652239
    {'degree': 2, 'field': [12, -1, 1], 'lmfdb_label': '77315.e2', 'torsion': [2, 2]}
  • id: 3652240
    {'degree': 4, 'field': [-188, 0, 47, 0, 1], 'lmfdb_label': '77315.e2', 'torsion': [4]}
  • id: 3652243
    {'degree': 8, 'field': [-212807, 67865, -69398, 3065, -1529, -7, 7, -4, 1], 'lmfdb_label': '77315.e2', 'torsion': [6]}
  • id: 3652241
    {'degree': 8, 'field': [5776, 0, 2452, 0, 437, 0, 37, 0, 1], 'lmfdb_label': '77315.e2', 'torsion': [2, 4]}
  • id: 3652242
    {'degree': 8, 'field': [111236, -87380, 14997, -3698, 2604, 52, 84, -2, 1], 'lmfdb_label': '77315.e2', 'torsion': [2, 4]}
  • id: 3652244
    {'degree': 16, 'field': [-2342336, 4698192, -4702476, 1855266, 861455, -1309616, 402248, -43720, 26160, -20798, 5460, 1736, -756, 28, 12, -8, 1], 'lmfdb_label': '77315.e2', 'torsion': [8]}
  • id: 3652245
    {'degree': 16, 'field': [585214791, -726868107, 295150554, -9180027, -20067276, -3450276, 6162384, -1775583, -3446, 118883, -22196, -4903, 2743, -349, 4, -4, 1], 'lmfdb_label': '77315.e2', '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: 1880585
    {'conductor': 77315, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '77315.e2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1880586
    {'conductor': 77315, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '77315.e2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1880587
    {'conductor': 77315, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '77315.e2', 'prime': 47, 'reduction_type': 0, '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: 2174569
    {'adelic_gens': [[396, 1, 559, 0], [1, 2, 2, 5], [1, 4, 0, 1], [941, 4, 566, 9], [989, 330, 328, 987], [1, 0, 4, 1], [1313, 4, 1312, 5], [3, 4, 8, 11]], 'adelic_image': '1316.12.0.?', 'conductor': 77315, 'lmfdb_label': '77315.e2', 'prime': 0}
  • id: 318989
    {'conductor': 77315, 'elladic_image': '2.3.0.1', 'lmfdb_label': '77315.e2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 3979567
    {'lmfdb_iso': '77315.e', 'p': 11, 'prec': 20, 'unit': 58584457603607989281, 'val': 1}
  • id: 3979568
    {'lmfdb_iso': '77315.e', 'p': 13, 'prec': 20, 'unit': 218002194922572828147, 'val': 1}
  • id: 3979565
    {'lmfdb_iso': '77315.e', 'p': 17, 'prec': 20, 'unit': 49465040007579790485112, 'val': 1}
  • id: 3979571
    {'lmfdb_iso': '77315.e', 'p': 19, 'prec': 20, 'unit': 1482205179087548745624378, 'val': 1}
  • id: 3979574
    {'lmfdb_iso': '77315.e', 'p': 23, 'prec': 20, 'unit': 6146159398482070586538660, 'val': 1}
  • id: 3979578
    {'lmfdb_iso': '77315.e', 'p': 31, 'prec': 20, 'unit': 15254711265362825593249407328, 'val': 1}
  • id: 3979564
    {'lmfdb_iso': '77315.e', 'p': 37, 'prec': 20, 'unit': 576094289570801864217222663173, 'val': 1}
  • id: 3979566
    {'lmfdb_iso': '77315.e', 'p': 41, 'prec': 20, 'unit': 520928498433037349181386734252, 'val': 1}
  • id: 3979570
    {'lmfdb_iso': '77315.e', 'p': 43, 'prec': 20, 'unit': 4932647645438523901953242921741, 'val': 1}
  • id: 3979572
    {'lmfdb_iso': '77315.e', 'p': 53, 'prec': 20, 'unit': 573515021551775553151575882942684, 'val': 1}
  • id: 3979576
    {'lmfdb_iso': '77315.e', 'p': 59, 'prec': 20, 'unit': 2207979622387930840458311858545313, 'val': 1}
  • id: 3979577
    {'lmfdb_iso': '77315.e', 'p': 61, 'prec': 20, 'unit': 564881294091725702463304030149828, 'val': 1}
  • id: 3979563
    {'lmfdb_iso': '77315.e', 'p': 67, 'prec': 20, 'unit': 10461806050882970508573987098268935, 'val': 1}
  • id: 3979573
    {'lmfdb_iso': '77315.e', 'p': 73, 'prec': 20, 'unit': 115137014793040733737182744606319061, 'val': 1}
  • id: 3979569
    {'lmfdb_iso': '77315.e', 'p': 79, 'prec': 20, 'unit': 785585139729370572332006656148986168, 'val': 1}
  • id: 3979562
    {'lmfdb_iso': '77315.e', 'p': 83, 'prec': 20, 'unit': 2624232130782080266125560255246859219, 'val': 1}
  • id: 3979575
    {'lmfdb_iso': '77315.e', 'p': 89, 'prec': 20, 'unit': 8828159107898653991959306129340528072, 'val': 1}
  • id: 3979561
    {'lmfdb_iso': '77315.e', 'p': 97, 'prec': 20, 'unit': 12211616359790518020691608869148416411, 'val': 1}