Elliptic curve data - 4800.q5

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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': '4800c', 'Clabel': '4800c1', 'Cnumber': 1, 'abc_quality': 1.1757189916348774, 'absD': 48000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 240, 'ainvs': [0, -1, 0, 67, 237], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4800, 'degree': 1024, 'elladic_images': ['16.48.0.150'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.15936667013719291464136898979', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [2048, 3], 'lmfdb_iso': '4800.q', 'lmfdb_label': '4800.q5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 1, 0], 'min_quad_twist_disc': 40, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '6.6.0.a.1', '8.24.0.ba.1', '12.12.0.g.1', '16.48.0.y.1', '24.48.0.bi.2', '40.48.0-8.ba.1.3', '48.96.1.dt.1', '80.96.0.?', '120.96.0.?', '240.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2498230461281090235054332691', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 75], [3, 4, 1600], [5, 14, 192]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2229749365464783638400374447', 'prec': 103}, 'szpiro_ratio': 2.9067630580757244, '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, -1, 0, 0, 0, 0, 0, 1, 0, -4, 0, -2, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, -1, 0, 0, -4, -2, -2, 4, 8, -6, 8, 6, -6, 4, 0, -2, -4, 2, -4, 8, -10, -8, -4, -6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 4800, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '4800.q', 'trace_hash': 229465160862369965}
• 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': '0.72706940358628777611249866685', 'prec': 103}, 'conductor': 4800, 'gens': [[13, 56, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2498230461281090235054332691', 'prec': 100}], 'lmfdb_label': '4800.q5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.3639002511783338651137987116', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0685342177209321149525512669598914929', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-3, 0, 1]], 'xcoord_integral_points': [-3, 13]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '7': [1, 3, 0], '11': [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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '4800.q5'}
• ec_torsion_growth •

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

  
  
  • id: 248836
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [4]}
  • id: 248835
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '4800.q5', 'torsion': [2, 2]}
  • id: 248837
    {'degree': 2, 'field': [30, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [4]}
  • id: 248839
    {'degree': 4, 'field': [25, 0, -20, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [8]}
  • id: 248840
    {'degree': 4, 'field': [25, 0, 0, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [8]}
  • id: 248838
    {'degree': 4, 'field': [100, 0, 10, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [2, 4]}
  • id: 248844
    {'degree': 8, 'field': [-1875, 0, -1250, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [6]}
  • id: 248842
    {'degree': 8, 'field': [529, 184, 146, -128, 100, -28, 14, -4, 1], 'lmfdb_label': '4800.q5', 'torsion': [8]}
  • id: 248841
    {'degree': 8, 'field': [625, 0, -500, 0, 75, 0, 10, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [2, 4]}
  • id: 248843
    {'degree': 8, 'field': [625, 0, 0, 0, -25, 0, 0, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [2, 8]}
  • id: 248846
    {'degree': 16, 'field': [1, -12, -60, 240, -80, -540, 288, 288, -657, -420, 360, 360, 64, -48, -24, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [16]}
  • id: 248847
    {'degree': 16, 'field': [4, -16, 32, 0, -44, 24, 112, 0, -126, 0, 200, 192, 58, -16, -12, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [16]}
  • id: 248848
    {'degree': 16, 'field': [13486, 10360, 24644, 6000, 18320, -1888, 9028, -3480, 3688, -1692, 1108, -416, 206, -60, 20, -4, 1], 'lmfdb_label': '4800.q5', 'torsion': [16]}
  • id: 248845
    {'degree': 16, 'field': [52036, 9472, 39432, 93968, 16584, -61752, -33800, 13160, 13860, -608, -2684, -144, 264, 28, -12, -4, 1], 'lmfdb_label': '4800.q5', 'torsion': [4, 8]}
  • id: 248850
    {'degree': 16, 'field': [544959, -2292492, 3967556, -3570124, 1616312, -22772, -389768, 217132, -55890, 9900, -3618, 1348, -272, 40, 10, -8, 1], 'lmfdb_label': '4800.q5', 'torsion': [12]}
  • id: 248849
    {'degree': 16, 'field': [3515625, 0, -2343750, 0, 1281250, 0, -187500, 0, 24375, 0, -2500, 0, 150, 0, 0, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [2, 6]}
  • id: 248851
    {'degree': 16, 'field': [3515625, 0, 7968750, 0, 3250000, 0, 656250, 0, 78750, 0, 7250, 0, 600, 0, 30, 0, 1], 'lmfdb_label': '4800.q5', 'torsion': [12]}
• 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: 91837
    {'conductor': 4800, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4800.q5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 91838
    {'conductor': 4800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4800.q5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 91839
    {'conductor': 4800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4800.q5', 'prime': 5, 'reduction_type': 0, '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: 1695275
    {'adelic_gens': [[5, 4, 236, 237], [143, 0, 0, 239], [136, 145, 95, 106], [141, 160, 170, 11], [225, 16, 224, 17], [1, 0, 16, 1], [15, 2, 142, 227], [1, 16, 0, 1], [239, 80, 60, 59]], 'adelic_image': '240.192.1.?', 'conductor': 4800, 'lmfdb_label': '4800.q5', 'prime': 0}
  • id: 23815
    {'conductor': 4800, 'elladic_image': '16.48.0.150', 'lmfdb_label': '4800.q5', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 174471
    {'lmfdb_iso': '4800.q', 'p': 11, 'prec': 20, 'unit': 60943333722651770392, 'val': 1}
  • id: 174469
    {'lmfdb_iso': '4800.q', 'p': 13, 'prec': 20, 'unit': 922415405603380870764, 'val': 1}
  • id: 174472
    {'lmfdb_iso': '4800.q', 'p': 17, 'prec': 20, 'unit': 180113860829963107367475, 'val': 1}
  • id: 174473
    {'lmfdb_iso': '4800.q', 'p': 19, 'prec': 20, 'unit': 539801142108374696039804, 'val': 1}
  • id: 174476
    {'lmfdb_iso': '4800.q', 'p': 23, 'prec': 20, 'unit': 29796951541351757598590756, 'val': 1}
  • id: 174468
    {'lmfdb_iso': '4800.q', 'p': 29, 'prec': 20, 'unit': 3991531822191242864406379211, 'val': 1}
  • id: 174480
    {'lmfdb_iso': '4800.q', 'p': 31, 'prec': 20, 'unit': 19008008477751227472014722077, 'val': 1}
  • id: 174464
    {'lmfdb_iso': '4800.q', 'p': 37, 'prec': 20, 'unit': 277080421457622375752145110018, 'val': 1}
  • id: 174466
    {'lmfdb_iso': '4800.q', 'p': 41, 'prec': 20, 'unit': 78178370229197170775222921662, 'val': 1}
  • id: 174467
    {'lmfdb_iso': '4800.q', 'p': 43, 'prec': 20, 'unit': 6199678019181694952034277908981, 'val': 1}
  • id: 174474
    {'lmfdb_iso': '4800.q', 'p': 53, 'prec': 20, 'unit': 256600103991867580127548212280928, 'val': 1}
  • id: 174478
    {'lmfdb_iso': '4800.q', 'p': 59, 'prec': 20, 'unit': 1801344544841032914144779297821281, 'val': 1}
  • id: 174479
    {'lmfdb_iso': '4800.q', 'p': 61, 'prec': 20, 'unit': 5757220290733134168115710861500975, 'val': 1}
  • id: 174463
    {'lmfdb_iso': '4800.q', 'p': 67, 'prec': 20, 'unit': 24311555777103770251759824145364087, 'val': 1}
  • id: 174465
    {'lmfdb_iso': '4800.q', 'p': 71, 'prec': 20, 'unit': 61205446482722322855712028515695224, 'val': 1}
  • id: 174475
    {'lmfdb_iso': '4800.q', 'p': 73, 'prec': 20, 'unit': 235176514435381451214708143087097272, 'val': 1}
  • id: 174470
    {'lmfdb_iso': '4800.q', 'p': 79, 'prec': 20, 'unit': 196654300069466970503936320003464961, 'val': 1}
  • id: 174462
    {'lmfdb_iso': '4800.q', 'p': 83, 'prec': 20, 'unit': 188297028266587737628418663688779448, 'val': 1}
  • id: 174477
    {'lmfdb_iso': '4800.q', 'p': 89, 'prec': 20, 'unit': 10570817693786707543189067791182890002, 'val': 1}
  • id: 174461
    {'lmfdb_iso': '4800.q', 'p': 97, 'prec': 20, 'unit': 14477952280761062775290147554772464598, 'val': 1}