Elliptic curve data - 265200.dz1

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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': '265200dz', 'Clabel': '265200dz7', 'Cnumber': 7, 'abc_quality': 1.0592098442882552, 'absD': 6605842932000000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 26520, 'ainvs': [0, 1, 0, -2636400002408, 1647649523114107188], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 265200, 'degree': 1911029760, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '5.2720632584797211289106990247', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'intrinsic_torsion': 2, 'iso_nlabel': 103, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [31664865542564944883878115208137569, 103216295812500], 'lmfdb_iso': '265200.dz', 'lmfdb_label': '265200.dz1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -6591000006, -205956849489264], 'min_quad_twist_disc': -20, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.4', '20.12.0-4.c.1.2', '26.6.0.b.1', '52.12.0.g.1', '60.96.0-12.c.4.7', '78.24.0.?', '136.12.0.?', '156.96.1.?', '260.24.0.?', '408.96.1.?', '680.24.0.?', '780.192.1.?', '1768.24.0.?', '2040.192.1.?', '5304.192.5.?', '8840.48.0.?', '26520.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '36.158118782125018190950307133', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 325], [3, 4, 6800], [5, 18, 10608], [13, 14, 20400], [17, 18, 15600]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.7741971217027256321930872366', 'prec': 100}, 'szpiro_ratio': 7.800531783757611, '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, -4, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 4, 0], 'aplist': [0, 1, 0, -4, 0, -1, -1, 4, 0, 6, 4, -2, 6, -4, 0, -6, 12, -10, -4, 12, 10, 16, -12, -6, 10], 'class_deg': 12, 'class_size': 8, 'conductor': 265200, 'isogeny_matrix': [[1, 2, 4, 3, 4, 6, 12, 12], [2, 1, 2, 6, 2, 3, 6, 6], [4, 2, 1, 12, 4, 6, 12, 3], [3, 6, 12, 1, 12, 2, 4, 4], [4, 2, 4, 12, 1, 6, 3, 12], [6, 3, 6, 2, 6, 1, 2, 2], [12, 6, 12, 4, 3, 2, 1, 4], [12, 6, 3, 4, 12, 2, 4, 1]], 'lmfdb_iso': '265200.dz', 'trace_hash': 849042677993205695}
• 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': '0.000026347780528038878071958684672', 'prec': 117}, 'conductor': 265200, 'gens': [[414072431860180444, 226576240615305000830213154, 391181]], 'heights': [{'__RealLiteral__': 0, 'data': '36.158118782125018190950307133', 'prec': 100}], 'lmfdb_label': '265200.dz1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.028129194738463994160993321710', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.1367901167912574891395409906501712241', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[937443, 0, 1]], 'xcoord_integral_points': [937443]}
• lmfdb_label 265200.dz1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11353124
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '265200.dz1', 'torsion': [4]}
  • id: 11353125
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [6]}
  • id: 11353122
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 2]}
  • id: 11353123
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '265200.dz1', 'torsion': [4]}
  • id: 11353128
    {'degree': 4, 'field': [1, 8, -7, -2, 1], 'lmfdb_label': '265200.dz1', 'torsion': [12]}
  • id: 11353126
    {'degree': 4, 'field': [4, 0, -9, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 4]}
  • id: 11353129
    {'degree': 4, 'field': [36, 0, -27, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [12]}
  • id: 11353127
    {'degree': 4, 'field': [129, 36, -35, -2, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 6]}
  • id: 11353130
    {'degree': 6, 'field': [374669, 18360, 75, -1224, 15, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [6]}
  • id: 11353134
    {'degree': 8, 'field': [196, 0, -360, 0, 197, 0, -30, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 12]}
  • id: 11353133
    {'degree': 8, 'field': [5606, -500, 9728, -18646, 9799, -574, 196, -4, 1], 'lmfdb_label': '265200.dz1', 'torsion': [8]}
  • id: 11353131
    {'degree': 8, 'field': [196249, 0, 28580, 0, -786, 0, 20, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 4]}
  • id: 11353132
    {'degree': 8, 'field': [3019879, 322852, -310912, -23696, 11389, 548, -178, -4, 1], 'lmfdb_label': '265200.dz1', 'torsion': [8]}
  • id: 11353135
    {'degree': 12, 'field': [188980009, 0, 10422750, 0, -2071425, 0, 30244, 0, 375, 0, 30, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [3, 6]}
  • id: 11353137
    {'degree': 12, 'field': [2249978221, 129224106, -40301109, -28181682, -1252122, 279990, 191295, 0, -888, -612, 9, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [12]}
  • id: 11353138
    {'degree': 12, 'field': [140515799824, 12379002336, 135959904, -917247240, -30337044, -179928, 2248209, 0, 255, -2448, 27, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [12]}
  • id: 11353136
    {'degree': 12, 'field': [142503078069, -4871328660, -604692657, 926495594, 1528530, -8683128, 2224871, 20886, -10626, 2368, 27, -6, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 6]}
  • id: 11353140
    {'degree': 16, 'field': [-7784729, 118302656, 186279890, -512347968, 25783502, 244478452, -30068222, -40346544, 5540335, 2848524, -390374, -94000, 12512, 1428, -184, -8, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 8]}
  • id: 11353143
    {'degree': 16, 'field': [62649, -3889440, 16997994, -18772284, -7750316, 16567416, 738102, -4585204, 212297, 557960, -48694, -32020, 3456, 840, -100, -8, 1], 'lmfdb_label': '265200.dz1', 'torsion': [24]}
  • id: 11353142
    {'degree': 16, 'field': [187388721, 0, 0, 0, -355914, 0, 0, 0, -13013, 0, 0, 0, -26, 0, 0, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 12]}
  • id: 11353139
    {'degree': 16, 'field': [210511081, 0, -57680520, 0, 9310450, 0, -826812, 0, 82563, 0, -1260, 0, 526, 0, 12, 0, 1], 'lmfdb_label': '265200.dz1', 'torsion': [4, 4]}
  • id: 11353141
    {'degree': 16, 'field': [11844738116, 5772171112, 14927727904, 3435531384, 197139322, 491950092, 115047848, -21729366, 12397481, -1107366, 426702, -31390, 9328, -374, 110, -4, 1], 'lmfdb_label': '265200.dz1', 'torsion': [2, 8]}
  • id: 11353144
    {'degree': 16, 'field': [870489147940, -9677893080, 6904073696, 5503358600, -2638882732, -141207732, 56774804, -8238228, 1990105, -1776, 46564, -22844, 1866, 868, -104, -8, 1], 'lmfdb_label': '265200.dz1', 'torsion': [24]}
  • id: 11353145
    {'degree': 18, 'field': [103499660938406641, 14216198630571102, 85063966069263150, 39130194103266704, 10871555306979285, 2413677826018662, 272136780866774, 15637789118670, 1292530423068, 18372173390, -6132441525, -349456110, -55407865, -1915740, -41295, -3526, 483, 0, 1], 'lmfdb_label': '265200.dz1', '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: 6573791
    {'conductor': 265200, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '265200.dz1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6573792
    {'conductor': 265200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '265200.dz1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6573793
    {'conductor': 265200, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '265200.dz1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6573794
    {'conductor': 265200, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '265200.dz1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6573795
    {'conductor': 265200, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '265200.dz1', 'prime': 17, '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: 3342502
    {'adelic_gens': [[1, 24, 0, 1], [1, 0, 24, 1], [12481, 21240, 1260, 16201], [1, 12, 12, 145], [15, 106, 25214, 17291], [18801, 3760, 3740, 10301], [26497, 24, 26496, 25], [20416, 15915, 13005, 15826], [5303, 0, 0, 26519], [22101, 12380, 20, 13341], [19889, 5280, 9270, 10319]], 'adelic_image': '26520.384.5.?', 'conductor': 265200, 'lmfdb_label': '265200.dz1', 'prime': 0}
  • id: 950281
    {'conductor': 265200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '265200.dz1', 'modell_image': '2B', 'prime': 2}
  • id: 950282
    {'conductor': 265200, 'elladic_image': '3.4.0.1', 'lmfdb_label': '265200.dz1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 265200.dz does not appear in ec_padic