Elliptic curve data - 315.a1

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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': '315b', 'Clabel': '315b3', 'Cnumber': 3, 'abc_quality': 0.9608739095359471, 'absD': 9568125, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [1, -1, 1, -1013, 12656], 'analytic_rank': 1, 'bad_primes': [3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 315, 'degree': 128, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.38334398490683156792257326164', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [157551496201, 13125], 'lmfdb_iso': '315.a', 'lmfdb_label': '315.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -113, -469], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.1', '28.12.0-4.c.1.1', '40.12.0.ba.1', '42.6.0.a.1', '84.24.0.?', '120.24.0.?', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.25941501140757438382702766045', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 63], [3, 8, 35], [5, 6, 63], [7, 8, 45]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.16596215942722327777504935682', 'prec': 107}, 'szpiro_ratio': 5.6278632129357185, '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, 0, 1, 0, 0, -6, -1, 0, -1, -2, 0, -8, 1], 'aplist': [-1, 0, -1, 1, 0, -6, -2, -8, -8, 2, 4, -2, 6, 4, -8, -10, -4, -2, 4, 12, -2, 8, 4, 6, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 315, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '315.a', 'trace_hash': 1279478226797432480}
• 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': '0.46454912389722548827752627617', 'prec': 103}, 'conductor': 315, 'gens': [[0, 112, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.25941501140757438382702766045', 'prec': 103}], 'lmfdb_label': '315.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.1956280654282147800552602950', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1391577592797016255172626839658745923', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[75, -79, 2]], 'xcoord_integral_points': [-18, 0, 18, 21, 25]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [3, 0], '7': [2, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '315.a1'}
• ec_torsion_growth •

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

  
  
  • id: 13226
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [4]}
  • id: 13225
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '315.a1', 'torsion': [2, 2]}
  • id: 13227
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [4]}
  • id: 13228
    {'degree': 4, 'field': [1, 0, -5, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [2, 4]}
  • id: 13232
    {'degree': 8, 'field': [-27, 0, 0, 0, 18, 0, -13, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [6]}
  • id: 13231
    {'degree': 8, 'field': [196, 0, 196, 0, 57, 0, 4, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [8]}
  • id: 13229
    {'degree': 8, 'field': [441, 0, 0, 0, 21, 0, 0, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [2, 4]}
  • id: 13230
    {'degree': 8, 'field': [15876, 0, -15876, 0, 2037, 0, -84, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [8]}
  • id: 13234
    {'degree': 16, 'field': [81, 0, 756, 0, 3213, 0, 5124, 0, 4288, 0, 1708, 0, 357, 0, 28, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [2, 8]}
  • id: 13236
    {'degree': 16, 'field': [225, 0, -504, 0, -720, 0, 219, 0, 480, 0, -195, 0, -26, 0, -5, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [2, 6]}
  • id: 13233
    {'degree': 16, 'field': [625, 250, 50, 1320, -211, -682, 1138, -474, -20, 228, -152, 46, 5, -12, 8, -4, 1], 'lmfdb_label': '315.a1', 'torsion': [4, 4]}
  • id: 13238
    {'degree': 16, 'field': [9801, 0, -20244, 0, 13072, 0, 3183, 0, -1980, 0, -283, 0, -3, 0, -6, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [12]}
  • id: 13237
    {'degree': 16, 'field': [2461761, 0, -4906566, 0, 3286935, 0, -652944, 0, -48891, 0, 13056, 0, -425, 0, -26, 0, 1], 'lmfdb_label': '315.a1', 'torsion': [12]}
  • id: 13235
    {'degree': 16, 'field': [15752961, 0, -210039480, 0, 181117377, 0, -46230912, 0, 5426064, 0, -331632, 0, 10689, 0, -168, 0, 1], 'lmfdb_label': '315.a1', '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: 2935
    {'conductor': 315, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '315.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2936
    {'conductor': 315, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '315.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2937
    {'conductor': 315, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '315.a1', 'prime': 7, '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: 1667071
    {'adelic_gens': [[323, 316, 362, 741], [1, 0, 8, 1], [833, 8, 832, 9], [1, 8, 0, 1], [1, 4, 4, 17], [248, 3, 365, 2], [337, 8, 508, 33], [7, 6, 834, 835], [739, 738, 538, 115], [272, 837, 275, 838]], 'adelic_image': '840.48.0.?', 'conductor': 315, 'lmfdb_label': '315.a1', 'prime': 0}
  • id: 1275
    {'conductor': 315, 'elladic_image': '4.6.0.1', 'lmfdb_label': '315.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3469
    {'lmfdb_iso': '315.a', 'p': 13, 'prec': 20, 'unit': 322709316073556599483, 'val': 1}
  • id: 3471
    {'lmfdb_iso': '315.a', 'p': 17, 'prec': 20, 'unit': 110797244048241590386438, 'val': 1}
  • id: 3472
    {'lmfdb_iso': '315.a', 'p': 19, 'prec': 20, 'unit': 1279513256598745755760227, 'val': 1}
  • id: 3476
    {'lmfdb_iso': '315.a', 'p': 23, 'prec': 20, 'unit': 2589140680813627762856208, 'val': 1}
  • id: 3468
    {'lmfdb_iso': '315.a', 'p': 29, 'prec': 20, 'unit': 4864432115551392721398705401, 'val': 1}
  • id: 3480
    {'lmfdb_iso': '315.a', 'p': 31, 'prec': 20, 'unit': 15039290071712060650411745814, 'val': 1}
  • id: 3464
    {'lmfdb_iso': '315.a', 'p': 37, 'prec': 20, 'unit': 527978275818368658264403057652, 'val': 1}
  • id: 3466
    {'lmfdb_iso': '315.a', 'p': 41, 'prec': 20, 'unit': 3168222332410010824174936742162, 'val': 1}
  • id: 3467
    {'lmfdb_iso': '315.a', 'p': 43, 'prec': 20, 'unit': 8545668128895767602253293367124, 'val': 1}
  • id: 3478
    {'lmfdb_iso': '315.a', 'p': 47, 'prec': 20, 'unit': 43286902427239396407670878428704, 'val': 1}
  • id: 3473
    {'lmfdb_iso': '315.a', 'p': 53, 'prec': 20, 'unit': 355753835361761857842704149943853, 'val': 1}
  • id: 3474
    {'lmfdb_iso': '315.a', 'p': 59, 'prec': 20, 'unit': 422419573237063318109372250681357, 'val': 1}
  • id: 3479
    {'lmfdb_iso': '315.a', 'p': 61, 'prec': 20, 'unit': 3525317002464994776409923268877057, 'val': 1}
  • id: 3463
    {'lmfdb_iso': '315.a', 'p': 67, 'prec': 20, 'unit': 16430478219998281539361020080072695, 'val': 1}
  • id: 3465
    {'lmfdb_iso': '315.a', 'p': 71, 'prec': 20, 'unit': 113937436636258398643065597731244028, 'val': 1}
  • id: 3475
    {'lmfdb_iso': '315.a', 'p': 73, 'prec': 20, 'unit': 241574028685805781544020350424596328, 'val': 1}
  • id: 3470
    {'lmfdb_iso': '315.a', 'p': 79, 'prec': 20, 'unit': 287624298948482865533336311765763801, 'val': 1}
  • id: 3462
    {'lmfdb_iso': '315.a', 'p': 83, 'prec': 20, 'unit': 2452018853068217954247705684756341303, 'val': 1}
  • id: 3477
    {'lmfdb_iso': '315.a', 'p': 89, 'prec': 20, 'unit': 373143132766500517810794846249403981, 'val': 1}
  • id: 3461
    {'lmfdb_iso': '315.a', 'p': 97, 'prec': 20, 'unit': 46599584280720894798351588591407503185, 'val': 1}