Elliptic curve data - 45.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
  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
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '45a', 'Clabel': '45a8', 'Cnumber': 8, 'abc_quality': 1.0594919023465201, 'absD': 156905298045, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, -1, 0, -990, 22765], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 45, 'degree': 32, 'elladic_images': ['32.96.0.67'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.84017575281115636767125824276', 'prec': 103}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-147281603041, 215233605], 'lmfdb_iso': '45.a', 'lmfdb_label': '45.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -110, -880], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.ba.2', '12.12.0-4.c.1.1', '16.48.0.u.2', '20.12.0.h.1', '24.48.0-8.ba.2.5', '32.96.0-16.u.2.4', '40.48.0.bm.2', '48.96.0-16.u.2.5', '60.24.0-20.h.1.1', '80.192.5.?', '96.192.1.?', '120.96.0.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 8, 5], [5, 6, 9]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562430', 'prec': 103}, 'szpiro_ratio': 8.818023394379875, '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, 0, -3, 0, -1, 4, 0, -2, 0, 0, -1, -2, 0, 4, 1], 'aplist': [1, 0, -1, 0, 4, -2, -2, 4, 0, 2, 0, -10, -10, 4, -8, 10, 4, -2, 12, 8, 10, 0, -12, 6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 45, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '45.a', 'trace_hash': 804981580358494444}
• 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': '0.18630847605146075848056189851', 'prec': 103}, 'conductor': 45, 'gens': [], 'heights': [], 'lmfdb_label': '45.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.92159087663963161474779346108', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.92159087663963161474779346108013593903', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-157, 157, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 1], '3': 'a', '5': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '45.a3'}
• ec_torsion_growth •

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

  
  
  • id: 1480
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [4]}
  • id: 1481
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '45.a3', 'torsion': [4]}
  • id: 1479
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [2, 2]}
  • id: 1484
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [8]}
  • id: 1482
    {'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [2, 4]}
  • id: 1483
    {'degree': 4, 'field': [25, 0, -20, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [8]}
  • id: 1490
    {'degree': 8, 'field': [-1, -4, 4, 1, -2, -1, 5, -4, 1], 'lmfdb_label': '45.a3', 'torsion': [6]}
  • id: 1485
    {'degree': 8, 'field': [25, 0, 0, 0, -5, 0, 0, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [2, 4]}
  • id: 1486
    {'degree': 8, 'field': [25, 0, 0, 0, 5, 0, 0, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [8]}
  • id: 1487
    {'degree': 8, 'field': [36, 0, 12, 0, 13, 0, -8, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [2, 8]}
  • id: 1489
    {'degree': 8, 'field': [225, 0, 1200, 0, 460, 0, 40, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [16]}
  • id: 1488
    {'degree': 8, 'field': [4225, 0, -2800, 0, 540, 0, -40, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [16]}
  • id: 1492
    {'degree': 16, 'field': [1, 2, 2, 24, 13, -74, 114, -58, -12, 44, -24, -2, 13, -12, 8, -4, 1], 'lmfdb_label': '45.a3', 'torsion': [2, 8]}
  • id: 1498
    {'degree': 16, 'field': [1, 7, 17, 11, -17, -21, 13, 19, -13, -19, 13, 21, -17, -11, 17, -7, 1], 'lmfdb_label': '45.a3', 'torsion': [12]}
  • id: 1497
    {'degree': 16, 'field': [9, 0, 9, 0, -20, 0, -87, 0, 105, 0, -17, 0, 15, 0, -6, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [12]}
  • id: 1494
    {'degree': 16, 'field': [25, 0, 0, 0, 25, 0, 0, 0, 30, 0, 0, 0, -5, 0, 0, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [16]}
  • id: 1493
    {'degree': 16, 'field': [625, 0, 0, 0, -200, 0, 0, 0, 39, 0, 0, 0, -8, 0, 0, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [16]}
  • id: 1496
    {'degree': 16, 'field': [625, 0, 375, 0, 25, 0, 100, 0, 150, 0, 115, 0, 55, 0, 15, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [2, 6]}
  • id: 1491
    {'degree': 16, 'field': [1296, 0, 2016, 0, 2560, 0, 1184, 0, 444, 0, -176, 0, 0, 0, -4, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [4, 4]}
  • id: 1495
    {'degree': 16, 'field': [22500, 0, -60000, 0, 59500, 0, -12000, 0, 3525, 0, -200, 0, 120, 0, 0, 0, 1], 'lmfdb_label': '45.a3', 'torsion': [2, 16]}
• 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: 209
    {'conductor': 45, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '45.a3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 210
    {'conductor': 45, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '45.a3', 'prime': 5, '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: 1665980
    {'adelic_gens': [[214, 3, 365, 268], [60, 31, 239, 324], [1, 0, 32, 1], [1, 32, 0, 1], [5, 28, 68, 381], [449, 32, 448, 33], [23, 18, 318, 395], [421, 32, 436, 33], [319, 448, 304, 447]], 'adelic_image': '480.768.13.?', 'conductor': 45, 'lmfdb_label': '45.a3', 'prime': 0}
  • id: 118
    {'conductor': 45, 'elladic_image': '32.96.0.67', 'lmfdb_label': '45.a3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 45.a does not appear in ec_padic