Elliptic curve data - 315.a3

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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': '315b1', 'Cnumber': 1, 'abc_quality': 0.9665903421508077, 'absD': 76545, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [1, -1, 1, -23, -34], 'analytic_rank': 1, 'bad_primes': [3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 315, 'degree': 32, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.30980319565311374149465885981', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [1771561, 105], 'lmfdb_iso': '315.a', 'lmfdb_label': '315.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -3, 1], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '28.12.0-4.c.1.2', '40.12.0.ba.1', '60.12.0-4.c.1.2', '120.24.0.?', '168.24.0.?', '210.6.0.?', '280.24.0.?', '420.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0376600456302975353081106418', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 8, 35], [5, 6, 63], [7, 8, 45]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.85910933998716858719228147827', 'prec': 107}, 'szpiro_ratio': 3.6468979508760584, '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': '1.8581964955889019531101051047', 'prec': 100}, 'conductor': 315, 'gens': [[6, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0376600456302975353081106418', 'prec': 100}], 'lmfdb_label': '315.a3', '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': 2, 'torsion_generators': [[-3, 1, 1]], 'xcoord_integral_points': [-3, -2, 6, 61]}
• 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.a3'}
• ec_torsion_growth •

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

  
  
  • id: 13203
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '315.a3', 'torsion': [2, 2]}
  • id: 13205
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '315.a3', 'torsion': [4]}
  • id: 13204
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '315.a3', 'torsion': [4]}
  • id: 13206
    {'degree': 4, 'field': [4, 0, 11, 0, 1], 'lmfdb_label': '315.a3', 'torsion': [2, 4]}
  • id: 13210
    {'degree': 8, 'field': [-27, 0, 0, 0, 18, 0, -13, 0, 1], 'lmfdb_label': '315.a3', 'torsion': [6]}
  • id: 13209
    {'degree': 8, 'field': [16, 0, 52, 0, 45, 0, 13, 0, 1], 'lmfdb_label': '315.a3', 'torsion': [8]}
  • id: 13208
    {'degree': 8, 'field': [36, -84, 70, -46, 39, -26, 15, -4, 1], 'lmfdb_label': '315.a3', 'torsion': [8]}
  • id: 13207
    {'degree': 8, 'field': [756, -6048, 7560, -1428, 109, 178, -30, -2, 1], 'lmfdb_label': '315.a3', 'torsion': [2, 4]}
  • id: 13216
    {'degree': 16, 'field': [1089, 0, 3024, 0, 9486, 0, -762, 0, 3375, 0, -762, 0, 43, 0, -3, 0, 1], 'lmfdb_label': '315.a3', 'torsion': [12]}
  • id: 13212
    {'degree': 16, 'field': [1516, 2364, -2365, -3250, 11978, -19284, 19871, -15870, 10183, -5460, 2599, -1082, 423, -140, 40, -8, 1], 'lmfdb_label': '315.a3', 'torsion': [2, 8]}
  • id: 13213
    {'degree': 16, 'field': [2116, 0, -1044, 0, 1805, 0, -2601, 0, 1239, 0, -306, 0, 95, 0, -9, 0, 1], 'lmfdb_label': '315.a3', 'torsion': [2, 8]}
  • id: 13215
    {'degree': 16, 'field': [2304, 0, 2496, 0, 8800, 0, 1248, 0, 525, 0, 143, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '315.a3', 'torsion': [12]}
  • id: 13211
    {'degree': 16, 'field': [34596, -185256, 496008, -985608, 1006053, -80538, 46866, -39954, -6677, -6772, 1124, 284, 523, -74, 2, -2, 1], 'lmfdb_label': '315.a3', 'torsion': [4, 4]}
  • id: 13214
    {'degree': 16, 'field': [700569, 0, -798174, 0, 91485, 0, 2403, 0, 1080, 0, 933, 0, 72, 0, 0, 0, 1], 'lmfdb_label': '315.a3', '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: 2929
    {'conductor': 315, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '315.a3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2930
    {'conductor': 315, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '315.a3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2931
    {'conductor': 315, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '315.a3', '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: 1667073
    {'adelic_gens': [[833, 8, 832, 9], [1, 0, 8, 1], [113, 108, 110, 527], [1, 8, 0, 1], [1, 4, 4, 17], [508, 1, 191, 6], [248, 3, 365, 2], [7, 6, 834, 835], [739, 738, 538, 115], [272, 837, 275, 838]], 'adelic_image': '840.48.0.?', 'conductor': 315, 'lmfdb_label': '315.a3', 'prime': 0}
  • id: 1277
    {'conductor': 315, 'elladic_image': '4.6.0.1', 'lmfdb_label': '315.a3', '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}