Elliptic curve data - 48400.l4

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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': '48400cn', 'Clabel': '48400cn2', 'Cnumber': 2, 'abc_quality': 0.8396384887826309, 'absD': 177156100000000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 1320, 'ainvs': [0, 1, 0, 11092, 459688], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 48400, 'degree': 138240, 'elladic_images': ['4.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4202900873806881428659414358', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [21296, 25], 'lmfdb_iso': '48400.l', 'lmfdb_label': '48400.l4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 4, 4], 'min_quad_twist_disc': 220, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.a.1', '6.12.0.a.1', '12.24.0.d.1', '20.12.0.d.1', '24.48.0.bh.1', '40.24.0.bc.1', '60.48.1.h.1', '88.12.0.?', '120.192.9.?', '132.48.0.?', '264.96.0.?', '330.24.0.?', '440.48.0.?', '660.96.1.?', '1320.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.8542921366587094924695045326', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3025], [5, 18, 1936], [11, 62, 400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0454746256088441894102314341', 'prec': 103}, 'szpiro_ratio': 3.6694785432646793, '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, -2, 0, 0, 0, -2, 0, 1, 0, 0, 0, 2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, -2, 0, -2, 0, 2, -6, -4, 6, -6, 4, -2, -6, 10, -6, 6, -12, -2, 2, 12, 2, 8, -6, -6, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 48400, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '48400.l', 'trace_hash': 1830441599807932152}
• 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': '0.058391778698910274319704038138', 'prec': 107}, 'conductor': 48400, 'gens': [[463, 10250, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.8542921366587094924695045326', 'prec': 100}], 'lmfdb_label': '48400.l4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.38083866645068687327162694553', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9357269548729429842795104030356112367', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-37, 0, 1]], 'xcoord_integral_points': [-37, 463]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [9, 0], '5': 'a', '7': [1, 0], '11': 'a', '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': '48400.l4'}
• ec_torsion_growth •

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

  
  
  • id: 2355883
    {'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '48400.l4', 'torsion': [6]}
  • id: 2355882
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '48400.l4', 'torsion': [2, 2]}
  • id: 2355884
    {'degree': 4, 'field': [-121, 0, -11, 0, 1], 'lmfdb_label': '48400.l4', 'torsion': [4]}
  • id: 2355885
    {'degree': 4, 'field': [196, 0, -27, 0, 1], 'lmfdb_label': '48400.l4', 'torsion': [2, 6]}
  • id: 2355886
    {'degree': 6, 'field': [4854, -1212, 1270, -170, 60, -2, 1], 'lmfdb_label': '48400.l4', 'torsion': [6]}
  • id: 2355889
    {'degree': 8, 'field': [229, -1502, -1030, 170, 226, 14, -22, -2, 1], 'lmfdb_label': '48400.l4', 'torsion': [12]}
  • id: 2355888
    {'degree': 8, 'field': [361, 608, 512, -198, 63, 22, 2, -2, 1], 'lmfdb_label': '48400.l4', 'torsion': [2, 4]}
  • id: 2355887
    {'degree': 8, 'field': [18056, -1712, -3336, -1104, 680, 128, -44, -4, 1], 'lmfdb_label': '48400.l4', 'torsion': [2, 4]}
  • id: 2355891
    {'degree': 12, 'field': [47961, 0, 54861, 0, 32530, 0, -495, 0, -70, 0, 21, 0, 1], 'lmfdb_label': '48400.l4', 'torsion': [2, 6]}
  • id: 2355890
    {'degree': 12, 'field': [1565001, 690552, 173349, 183060, 44880, 2772, -581, -722, 230, -110, -1, -2, 1], 'lmfdb_label': '48400.l4', 'torsion': [3, 6]}
  • id: 2355892
    {'degree': 16, 'field': [3721, 0, 312456, 0, 474346, 0, 300716, 0, 94999, 0, 15724, 0, 1378, 0, 60, 0, 1], 'lmfdb_label': '48400.l4', 'torsion': [4, 4]}
  • id: 2355895
    {'degree': 16, 'field': [6561, -4374, 1458, -6804, 6642, 54, 2016, -1806, 43, -602, 224, 2, 82, -28, 2, -2, 1], 'lmfdb_label': '48400.l4', 'torsion': [2, 12]}
  • id: 2355893
    {'degree': 16, 'field': [205181, 421768, -58918, -142776, 1067258, -1007420, 706226, -294668, 14303, 37364, -22186, 6472, -1112, 48, 28, -8, 1], 'lmfdb_label': '48400.l4', 'torsion': [8]}
  • id: 2355894
    {'degree': 16, 'field': [5354596, 0, -4778248, 0, 1981692, 0, -492328, 0, 80493, 0, -9004, 0, 698, 0, -36, 0, 1], 'lmfdb_label': '48400.l4', 'torsion': [2, 12]}
  • id: 2355896
    {'degree': 18, 'field': [-95738586136, -68761531008, 12784388472, 9362090776, 1702670136, 861543744, -316512140, 80469840, -14163432, 464300, -491652, -259296, 55304, -1488, 1812, -332, 0, 0, 1], 'lmfdb_label': '48400.l4', 'torsion': [18]}
• 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: 1155890
    {'conductor': 48400, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48400.l4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1155891
    {'conductor': 48400, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '48400.l4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1155892
    {'conductor': 48400, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48400.l4', 'prime': 11, '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: 1986273
    {'adelic_gens': [[1297, 24, 1296, 25], [1299, 616, 286, 243], [1209, 836, 1177, 307], [13, 24, 612, 13], [483, 110, 1276, 1099], [661, 264, 726, 265], [1, 24, 0, 1], [15, 16, 314, 335], [1, 0, 24, 1], [119, 0, 0, 1319]], 'adelic_image': '1320.384.9.?', 'conductor': 48400, 'lmfdb_label': '48400.l4', 'prime': 0}
  • id: 208617
    {'conductor': 48400, 'elladic_image': '4.6.0.5', 'lmfdb_label': '48400.l4', 'modell_image': '2B', 'prime': 2}
  • id: 208618
    {'conductor': 48400, 'elladic_image': '3.4.0.1', 'lmfdb_label': '48400.l4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2428999
    {'lmfdb_iso': '48400.l', 'p': 7, 'prec': 20, 'unit': 10240251837266362, 'val': 1}
  • id: 2429003
    {'lmfdb_iso': '48400.l', 'p': 13, 'prec': 20, 'unit': 1045737757362577547804, 'val': 1}
  • id: 2429005
    {'lmfdb_iso': '48400.l', 'p': 17, 'prec': 20, 'unit': 85858682561032059502415, 'val': 1}
  • id: 2429006
    {'lmfdb_iso': '48400.l', 'p': 19, 'prec': 20, 'unit': 1163575792370816957710353, 'val': 1}
  • id: 2429010
    {'lmfdb_iso': '48400.l', 'p': 23, 'prec': 20, 'unit': 38972806353770269419509127, 'val': 1}
  • id: 2429002
    {'lmfdb_iso': '48400.l', 'p': 29, 'prec': 20, 'unit': 1936916312447271894945038668, 'val': 1}
  • id: 2429015
    {'lmfdb_iso': '48400.l', 'p': 31, 'prec': 20, 'unit': 6868540091517825777072738791, 'val': 1}
  • id: 2428998
    {'lmfdb_iso': '48400.l', 'p': 37, 'prec': 20, 'unit': 337931739087168192068749841675, 'val': 1}
  • id: 2429000
    {'lmfdb_iso': '48400.l', 'p': 41, 'prec': 20, 'unit': 2295659018602005013970907794471, 'val': 1}
  • id: 2429001
    {'lmfdb_iso': '48400.l', 'p': 43, 'prec': 20, 'unit': 7382435627622430401260410061919, 'val': 1}
  • id: 2429013
    {'lmfdb_iso': '48400.l', 'p': 47, 'prec': 20, 'unit': 34158027604417725632125940739423, 'val': 1}
  • id: 2429007
    {'lmfdb_iso': '48400.l', 'p': 53, 'prec': 20, 'unit': 171995059933966486730356616461667, 'val': 1}
  • id: 2429008
    {'lmfdb_iso': '48400.l', 'p': 59, 'prec': 20, 'unit': 3906684656053608392050839370180677, 'val': 1}
  • id: 2429014
    {'lmfdb_iso': '48400.l', 'p': 61, 'prec': 20, 'unit': 919362298171572707321944882736494, 'val': 1}
  • id: 2428997
    {'lmfdb_iso': '48400.l', 'p': 67, 'prec': 20, 'unit': 9934884653818175986531739557856735, 'val': 1}
  • id: 2429012
    {'lmfdb_iso': '48400.l', 'p': 71, 'prec': 20, 'unit': 23137439775135015886019461343664850, 'val': 1}
  • id: 2429009
    {'lmfdb_iso': '48400.l', 'p': 73, 'prec': 20, 'unit': 9957803931066750302401508566907623, 'val': 1}
  • id: 2429004
    {'lmfdb_iso': '48400.l', 'p': 79, 'prec': 20, 'unit': 343235383035500531541428775146253626, 'val': 1}
  • id: 2428996
    {'lmfdb_iso': '48400.l', 'p': 83, 'prec': 20, 'unit': 2424017507239590204633818857783758043, 'val': 1}
  • id: 2429011
    {'lmfdb_iso': '48400.l', 'p': 89, 'prec': 20, 'unit': 8618436374364193532134827540991085091, 'val': 1}
  • id: 2428995
    {'lmfdb_iso': '48400.l', 'p': 97, 'prec': 20, 'unit': 18453938448400478361152151394420005656, 'val': 1}