Elliptic curve data - 47808.p2

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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': '47808be', 'Clabel': '47808be2', 'Cnumber': 2, 'abc_quality': 0.9566948704435101, 'absD': 4443215855616, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1992, 'ainvs': [0, 0, 0, -1836, -105840], 'analytic_rank': 2, 'bad_primes': [2, 3, 83], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 47808, 'degree': 55296, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1103316252412117110599222037', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [-1061208, 6889], 'lmfdb_iso': '47808.p', 'lmfdb_label': '47808.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -51, 490], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.b.1', '664.6.0.?', '996.6.0.?', '1992.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '6.4224177487462547988169006398', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 2, 5312], [83, 84, 576]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.58006156695980219425805187582', 'prec': 107}, 'szpiro_ratio': 3.4025697591878274, '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, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -6, 0], 'aplist': [0, 0, -2, 0, -4, 0, 0, -6, -2, 6, -8, -2, -4, 2, -4, -6, 4, -2, 10, -4, -2, -8, -1, -14, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 47808, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '47808.p', 'trace_hash': 539352227058552297}
• 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': '0.10853709766449252623568877294', 'prec': 103}, 'conductor': 47808, 'gens': [[114, 1080, 1], [76, 440, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7885039923984203466297128801', 'prec': 100}, {'__RealLiteral__': 0, 'data': '4.0104024773007767562839396204', 'prec': 100}], 'lmfdb_label': '47808.p2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.32489001641623975564852799898', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.3463176312884811837544400631099508030', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[60, 0, 1]], 'xcoord_integral_points': [60, 76, 114, 226, 1410]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [4, 4, 0], '11': [2, 0], '13': [2, 2, 0], '17': [2, 2, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0], '83': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '47808.p2'}
• ec_torsion_growth •

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

  
  
  • id: 2331099
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '47808.p2', 'torsion': [2, 2]}
  • id: 2331100
    {'degree': 4, 'field': [-6, 0, 15, 0, 1], 'lmfdb_label': '47808.p2', 'torsion': [4]}
  • id: 2331103
    {'degree': 8, 'field': [-108, 0, 360, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '47808.p2', 'torsion': [6]}
  • id: 2331101
    {'degree': 8, 'field': [319, 524, 622, -520, 187, -16, -2, -4, 1], 'lmfdb_label': '47808.p2', 'torsion': [2, 4]}
  • id: 2331102
    {'degree': 8, 'field': [3600, 0, 2736, 0, 609, 0, 54, 0, 1], 'lmfdb_label': '47808.p2', 'torsion': [2, 4]}
  • id: 2331105
    {'degree': 16, 'field': [68121, 0, 141324, 0, 54796, 0, 41628, 0, 12402, 0, -148, 0, 12, 0, 12, 0, 1], 'lmfdb_label': '47808.p2', 'torsion': [2, 6]}
  • id: 2331104
    {'degree': 16, 'field': [2232036, 0, -66961080, 0, 35425728, 0, 16628220, 0, 2219589, 0, 152820, 0, 5898, 0, 120, 0, 1], 'lmfdb_label': '47808.p2', 'torsion': [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: 1142256
    {'conductor': 47808, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '47808.p2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1142257
    {'conductor': 47808, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '47808.p2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1142258
    {'conductor': 47808, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47808.p2', 'prime': 83, 'reduction_type': -1, '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: 1982696
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [1081, 4, 170, 9], [1989, 4, 1988, 5], [1745, 250, 248, 1743], [2, 1, 995, 0], [668, 1, 1327, 0]], 'adelic_image': '1992.12.0.?', 'conductor': 47808, 'lmfdb_label': '47808.p2', 'prime': 0}
  • id: 206457
    {'conductor': 47808, 'elladic_image': '2.3.0.1', 'lmfdb_label': '47808.p2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2400776
    {'lmfdb_iso': '47808.p', 'p': 5, 'prec': 20, 'unit': 11383389086854, 'val': 2}
  • id: 2400783
    {'lmfdb_iso': '47808.p', 'p': 11, 'prec': 20, 'unit': 50054840890610156189, 'val': 2}
  • id: 2400785
    {'lmfdb_iso': '47808.p', 'p': 19, 'prec': 20, 'unit': 1657494607694850769009277, 'val': 2}
  • id: 2400788
    {'lmfdb_iso': '47808.p', 'p': 23, 'prec': 20, 'unit': 58061723293497268962791021, 'val': 2}
  • id: 2400781
    {'lmfdb_iso': '47808.p', 'p': 29, 'prec': 20, 'unit': 1295685163361712803871554509, 'val': 2}
  • id: 2400778
    {'lmfdb_iso': '47808.p', 'p': 31, 'prec': 20, 'unit': 10505721690172412192955252418, 'val': 2}
  • id: 2400792
    {'lmfdb_iso': '47808.p', 'p': 37, 'prec': 20, 'unit': 263616565052841454955710429473, 'val': 2}
  • id: 2400779
    {'lmfdb_iso': '47808.p', 'p': 41, 'prec': 20, 'unit': 3151850601785176425100675722830, 'val': 2}
  • id: 2400780
    {'lmfdb_iso': '47808.p', 'p': 43, 'prec': 20, 'unit': 9795224795338949943082888875991, 'val': 2}
  • id: 2400790
    {'lmfdb_iso': '47808.p', 'p': 47, 'prec': 20, 'unit': 44449683883760603113276854656929, 'val': 2}
  • id: 2400786
    {'lmfdb_iso': '47808.p', 'p': 53, 'prec': 20, 'unit': 432144202380664962653118434269158, 'val': 2}
  • id: 2400784
    {'lmfdb_iso': '47808.p', 'p': 59, 'prec': 20, 'unit': 4216266868075018506176236934440613, 'val': 2}
  • id: 2400791
    {'lmfdb_iso': '47808.p', 'p': 61, 'prec': 20, 'unit': 7002459596573593863770383305647698, 'val': 2}
  • id: 2400775
    {'lmfdb_iso': '47808.p', 'p': 67, 'prec': 20, 'unit': 42885122425337609827390141888716256, 'val': 2}
  • id: 2400777
    {'lmfdb_iso': '47808.p', 'p': 71, 'prec': 20, 'unit': 64084501915634941788379387952615204, 'val': 2}
  • id: 2400787
    {'lmfdb_iso': '47808.p', 'p': 73, 'prec': 20, 'unit': 221998804641943709645764457333121683, 'val': 2}
  • id: 2400782
    {'lmfdb_iso': '47808.p', 'p': 79, 'prec': 20, 'unit': 300274459527580391133796775173007396, 'val': 2}
  • id: 2400789
    {'lmfdb_iso': '47808.p', 'p': 89, 'prec': 20, 'unit': 10465182071312141058820225219700540858, 'val': 2}
  • id: 2400774
    {'lmfdb_iso': '47808.p', 'p': 97, 'prec': 20, 'unit': 3686267910667056829674029714691951530, 'val': 2}