Elliptic curve data - 193600.dx4

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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': '193600cr', 'Clabel': '193600cr3', 'Cnumber': 3, 'abc_quality': 1.1038914936992343, 'absD': 53589720250000000000000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 880, 'ainvs': [0, 0, 0, -31786700, 358898826000], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 193600, 'degree': 53084160, 'elladic_images': ['8.24.0.66'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6183461470610659853296867838', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 101, 'isogeny_degrees': [1, 2, 4], 'jinv': [-1957960715364, 29541015625], 'lmfdb_iso': '193600.dx', 'lmfdb_label': '193600.dx4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -2627, 269646], 'min_quad_twist_disc': 440, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0-4.d.1.5', '40.48.0-40.w.1.6', '44.24.0.d.1', '80.96.0.?', '88.48.0.?', '440.96.1.?', '880.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.9141144114549139442009298662', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3025], [5, 18, 7744], [11, 72, 1600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.69048331369823678010869249959', 'prec': 103}, 'szpiro_ratio': 5.482029585431913, '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, 0, 0, -4, 0, -3, 0, 0, 0, -6, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 0, -4, 0, -6, -6, -4, 4, -2, -8, -10, -10, 0, 4, -10, -4, -2, 8, 0, -14, -16, -8, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 193600, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '193600.dx', 'trace_hash': 1450072138601567853}
• 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': '0.00071968834478921405322251154788', 'prec': 113}, 'conductor': 193600, 'gens': [[1221, 567369, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.9141144114549139442009298662', 'prec': 100}], 'lmfdb_label': '193600.dx4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.053290765475727109544312887978', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4738337982927551644630365756277171674', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-8580, 0, 1]], 'xcoord_integral_points': [-8580, 1221]}
• lmfdb_label 193600.dx4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8516661
    {'degree': 2, 'field': [-110, 0, 1], 'lmfdb_label': '193600.dx4', 'torsion': [4]}
  • id: 8516660
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '193600.dx4', 'torsion': [2, 2]}
  • id: 8516662
    {'degree': 2, 'field': [110, 0, 1], 'lmfdb_label': '193600.dx4', 'torsion': [4]}
  • id: 8516663
    {'degree': 4, 'field': [3025, 0, 0, 0, 1], 'lmfdb_label': '193600.dx4', 'torsion': [2, 4]}
  • id: 8516667
    {'degree': 8, 'field': [-3630000, 0, 396000, 0, 6600, 0, 0, 0, 1], 'lmfdb_label': '193600.dx4', 'torsion': [6]}
  • id: 8516665
    {'degree': 8, 'field': [361, 0, -604, 0, 207, 0, -26, 0, 1], 'lmfdb_label': '193600.dx4', 'torsion': [8]}
  • id: 8516664
    {'degree': 8, 'field': [881, 692, -588, -220, 141, -40, 18, -4, 1], 'lmfdb_label': '193600.dx4', 'torsion': [4, 4]}
  • id: 8516666
    {'degree': 8, 'field': [14641, 0, 7986, 0, 847, 0, 44, 0, 1], 'lmfdb_label': '193600.dx4', 'torsion': [8]}
  • id: 8516669
    {'degree': 16, 'field': [3721, 0, 312456, 0, 474346, 0, 300716, 0, 94999, 0, 15724, 0, 1378, 0, 60, 0, 1], 'lmfdb_label': '193600.dx4', 'torsion': [2, 8]}
  • id: 8516668
    {'degree': 16, 'field': [18241441, 4031824, -2885798, -2255768, 1027002, 152104, -109534, 62756, -27061, 1612, 5094, -2268, -168, 224, -12, -8, 1], 'lmfdb_label': '193600.dx4', 'torsion': [2, 8]}
  • id: 8516672
    {'degree': 16, 'field': [297385375, -79981000, 571267050, 294448300, 379701320, 116676240, -7367276, -2940640, 52428, 94832, 42202, 4128, -238, -272, -12, -4, 1], 'lmfdb_label': '193600.dx4', 'torsion': [12]}
  • id: 8516670
    {'degree': 16, 'field': [3417091786, -386059616, 205037828, -10193616, 108301346, -28107652, 4283752, 293748, 575236, -316488, 51562, 2632, -2974, 336, 8, -4, 1], 'lmfdb_label': '193600.dx4', 'torsion': [2, 6]}
  • id: 8516671
    {'degree': 16, 'field': [9150625000000, 0, -385990000000, 0, 1936000000, 0, -84700000, 0, 19360000, 0, -847000, 0, 18700, 0, -220, 0, 1], 'lmfdb_label': '193600.dx4', '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: 4794673
    {'conductor': 193600, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '193600.dx4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4794674
    {'conductor': 193600, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '193600.dx4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4794675
    {'conductor': 193600, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '193600.dx4', '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: 2906562
    {'adelic_gens': [[1, 16, 0, 1], [207, 108, 104, 219], [384, 479, 47, 696], [703, 864, 516, 687], [465, 714, 726, 173], [1, 12, 4, 49], [1, 0, 16, 1], [5, 16, 64, 205], [865, 16, 864, 17]], 'adelic_image': '880.192.3.?', 'conductor': 193600, 'lmfdb_label': '193600.dx4', 'prime': 0}
  • id: 720852
    {'conductor': 193600, 'elladic_image': '8.24.0.66', 'lmfdb_label': '193600.dx4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 193600.dx does not appear in ec_padic