Elliptic curve data - 45738.p1

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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': '45738bh', 'Clabel': '45738bh1', 'Cnumber': 1, 'abc_quality': 1.0020635302334207, 'absD': 222381690756873189696, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 42, 'ainvs': [1, -1, 0, -5253540, -4577564656], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 45738, 'degree': 1596672, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7097632856813599665628046537', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1], 'jinv': [3800555813043, 52706752], 'lmfdb_iso': '45738.p', 'lmfdb_label': '45738.p1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -4824, -126208], 'min_quad_twist_disc': 33, 'modell_images': [], 'modm_images': ['42.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2203710348102875076458029490', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 22869], [3, 2, 77], [7, 8, 6534], [11, 52, 378]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.28720722064803066864174167403', 'prec': 103}, 'szpiro_ratio': 5.408493737220415, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 0, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, -1], 'aplist': [-1, 0, -1, -1, 0, 2, 2, 0, 4, 4, -2, 7, -5, 4, 11, 6, -15, 4, 3, -8, 4, -15, 3, -9, -14], 'class_deg': 1, 'class_size': 1, 'conductor': 45738, 'isogeny_matrix': [[1]], 'lmfdb_iso': '45738.p', 'trace_hash': 88992306299513963}
• 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': '0.0044292430820528746662100646383', 'prec': 110}, 'conductor': 45738, 'gens': [[-1361, 7759, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2203710348102875076458029490', 'prec': 100}], 'lmfdb_label': '45738.p1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.099804730668061285227011927263', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9888635960232949161447613869898746940', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [], 'xcoord_integral_points': [-1361]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 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': '45738.p1'}
• ec_torsion_growth •

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

  
  
  • id: 2233561
    {'degree': 3, 'field': [-44, -33, 0, 1], 'lmfdb_label': '45738.p1', 'torsion': [2]}
  • id: 2233562
    {'degree': 6, 'field': [-2924, -642, 597, 89, -42, -3, 1], 'lmfdb_label': '45738.p1', 'torsion': [2, 2]}
  • id: 2233563
    {'degree': 8, 'field': [-48, 0, -57, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '45738.p1', 'torsion': [3]}
  • id: 2233564
    {'degree': 12, 'field': [478821, 0, 730278, 0, 186423, 0, 13476, 0, -381, 0, -42, 0, 1], 'lmfdb_label': '45738.p1', 'torsion': [4]}
• 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: 1089828
    {'conductor': 45738, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '45738.p1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1089829
    {'conductor': 45738, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '45738.p1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1089830
    {'conductor': 45738, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '45738.p1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1089831
    {'conductor': 45738, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '45738.p1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'adelic_gens': [[1, 1, 41, 0], [1, 2, 0, 1], [31, 2, 31, 3], [1, 0, 2, 1], [41, 2, 40, 3], [29, 2, 29, 3]], 'adelic_image': '42.2.0.?', 'conductor': 45738, 'lmfdb_label': '45738.p1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2289054
    {'lmfdb_iso': '45738.p', 'p': 5, 'prec': 20, 'unit': 18619252048689, 'val': 1}
  • id: 2289060
    {'lmfdb_iso': '45738.p', 'p': 13, 'prec': 20, 'unit': 490963987112425932619, 'val': 1}
  • id: 2289062
    {'lmfdb_iso': '45738.p', 'p': 17, 'prec': 20, 'unit': 165434755790483724967618, 'val': 1}
  • id: 2289067
    {'lmfdb_iso': '45738.p', 'p': 23, 'prec': 20, 'unit': 67564919768367154729620475, 'val': 1}
  • id: 2289059
    {'lmfdb_iso': '45738.p', 'p': 29, 'prec': 20, 'unit': 4844819918971894832665536827, 'val': 1}
  • id: 2289056
    {'lmfdb_iso': '45738.p', 'p': 31, 'prec': 20, 'unit': 1821361394044854616444766336, 'val': 1}
  • id: 2289071
    {'lmfdb_iso': '45738.p', 'p': 37, 'prec': 20, 'unit': 368836928010620841151431659545, 'val': 1}
  • id: 2289057
    {'lmfdb_iso': '45738.p', 'p': 41, 'prec': 20, 'unit': 3528052236110834087957919313541, 'val': 1}
  • id: 2289058
    {'lmfdb_iso': '45738.p', 'p': 43, 'prec': 20, 'unit': 362311774411853513843895138585, 'val': 1}
  • id: 2289069
    {'lmfdb_iso': '45738.p', 'p': 47, 'prec': 20, 'unit': 45422815895725177058233368415479, 'val': 1}
  • id: 2289064
    {'lmfdb_iso': '45738.p', 'p': 53, 'prec': 20, 'unit': 524529548928261968625942264008120, 'val': 1}
  • id: 2289065
    {'lmfdb_iso': '45738.p', 'p': 59, 'prec': 20, 'unit': 4182108446099830475444269497746719, 'val': 1}
  • id: 2289070
    {'lmfdb_iso': '45738.p', 'p': 61, 'prec': 20, 'unit': 6482329060612800840098889465569282, 'val': 1}
  • id: 2289053
    {'lmfdb_iso': '45738.p', 'p': 67, 'prec': 20, 'unit': 248329834318448924204937801617630, 'val': 1}
  • id: 2289055
    {'lmfdb_iso': '45738.p', 'p': 71, 'prec': 20, 'unit': 48849249917610181749532623013405584, 'val': 1}
  • id: 2289066
    {'lmfdb_iso': '45738.p', 'p': 73, 'prec': 20, 'unit': 149073697066793762536791812135497731, 'val': 1}
  • id: 2289061
    {'lmfdb_iso': '45738.p', 'p': 79, 'prec': 20, 'unit': 706964090657335479259241577148508932, 'val': 1}
  • id: 2289063
    {'lmfdb_iso': '45738.p', 'p': 83, 'prec': 20, 'unit': 2397516705232229161306754382170742569, 'val': 1}
  • id: 2289068
    {'lmfdb_iso': '45738.p', 'p': 89, 'prec': 20, 'unit': 3900632982511903891467286071833975055, 'val': 1}
  • id: 2289052
    {'lmfdb_iso': '45738.p', 'p': 97, 'prec': 20, 'unit': 1189660984563574349043153776262024125, 'val': 1}