Elliptic curve data - 73920.de4

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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': '73920fo', 'Clabel': '73920fo3', 'Cnumber': 3, 'abc_quality': 1.0150912911963035, 'absD': 1763104358400000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, -1, 0, 300575, 7530625], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 73920, 'degree': 1179648, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1905267035565958116590838004', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 82, 'isogeny_degrees': [1, 2, 4], 'jinv': [11456208593737991, 6725709375000], 'lmfdb_iso': '73920.de', 'lmfdb_label': '73920.de4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 4697, -12947], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '24.24.0-24.v.1.2', '88.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 4, 24640], [5, 6, 14784], [7, 8, 10560], [11, 12, 6720]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1508059327166778475332356182', 'prec': 100}, 'szpiro_ratio': 4.4113023020895685, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 0, -1, 0, 1, 0, 1, 0, 6, 0, -1, 0, 6, 0, 0, 0], 'aplist': [0, -1, 1, -1, 1, 6, 6, 0, 4, -2, 0, 2, -2, -8, -12, 6, 4, -2, -12, 4, -6, -8, 12, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 73920, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '73920.de', 'trace_hash': 1136964722154297256}
• 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': '0.012512171266253818133036631745', 'prec': 107}, 'conductor': 73920, 'gens': [], 'heights': [], 'lmfdb_label': '73920.de4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16071101196088886872612003561', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5713761913742218996179205698177784779', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[525, 17600, 1]], 'xcoord_integral_points': [-25, 525]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [3, 0], '7': [0, 0], '11': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '73920.de4'}
• ec_torsion_growth •

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

  
  
  • id: 3499950
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '73920.de4', 'torsion': [2, 4]}
  • id: 3499951
    {'degree': 4, 'field': [-24, 0, 16, 0, 1], 'lmfdb_label': '73920.de4', 'torsion': [8]}
  • id: 3499955
    {'degree': 8, 'field': [-768, 0, -1688, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '73920.de4', 'torsion': [12]}
  • id: 3499954
    {'degree': 8, 'field': [3844, 0, -350, 0, -159, 0, 28, 0, 1], 'lmfdb_label': '73920.de4', 'torsion': [2, 8]}
  • id: 3499953
    {'degree': 8, 'field': [7569, 0, -2316, 0, 352, 0, -28, 0, 1], 'lmfdb_label': '73920.de4', 'torsion': [2, 8]}
  • id: 3499952
    {'degree': 8, 'field': [87025, 0, -3524, 0, 594, 0, 4, 0, 1], 'lmfdb_label': '73920.de4', 'torsion': [4, 4]}
  • id: 3499957
    {'degree': 16, 'field': [51840000, 0, -14592000, 0, -1611200, 0, 4101504, 0, 479232, 0, 11024, 0, 816, 0, 48, 0, 1], 'lmfdb_label': '73920.de4', 'torsion': [2, 12]}
  • id: 3499956
    {'degree': 16, 'field': [376515216, 0, -23953539456, 0, -7579357632, 0, -771503040, 0, -10616814, 0, 473040, 0, -11368, 0, 128, 0, 1], 'lmfdb_label': '73920.de4', 'torsion': [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: 1794465
    {'conductor': 73920, 'conductor_valuation': 6, 'discriminant_valuation': 21, 'j_denominator_valuation': 3, 'kodaira_symbol': -15, 'lmfdb_label': '73920.de4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1794466
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '73920.de4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1794467
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '73920.de4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1794468
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '73920.de4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1794469
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '73920.de4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2152219
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 258, 259], [257, 8, 256, 9], [32, 157, 95, 66], [92, 1, 199, 6], [29, 32, 142, 27], [145, 8, 52, 33]], 'adelic_image': '264.48.0.?', 'conductor': 73920, 'lmfdb_label': '73920.de4', 'prime': 0}
  • id: 305810
    {'conductor': 73920, 'elladic_image': '4.12.0.7', 'lmfdb_label': '73920.de4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 73920.de does not appear in ec_padic