Elliptic curve data - 203280.de5

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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': '203280cj', 'Clabel': '203280cj2', 'Cnumber': 2, 'abc_quality': 0.9765179895036278, 'absD': 1960221078579456000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, -1, 0, -30496880, 64798471872], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 203280, 'degree': 13271040, 'elladic_images': ['4.12.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0274959806376192870067081727', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 82, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [432288716775559561, 270140062500], 'lmfdb_iso': '203280.de', 'lmfdb_label': '203280.de5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -15753, 759256], 'min_quad_twist_disc': 44, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '4.12.0-2.a.1.1', '6.24.0.a.1', '12.48.0-6.a.1.1', '24.96.0-24.o.2.1', '132.96.0.?', '264.192.1.?', '420.96.0.?', '840.192.1.?', '1540.24.0.?', '4620.192.1.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 13, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6255767748537774471980372644', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 121], [3, 4, 13552], [5, 6, 40656], [7, 8, 29040], [11, 72, 1680]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1354011636784887055585042623', 'prec': 100}, 'szpiro_ratio': 5.180105435467722, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 1, 0, 1, 0, 1, 0, 0, 0, -2, 0, -1, 0, -6, 0, -4, 0], 'aplist': [0, -1, 1, 1, 0, -2, -6, -4, 0, -6, 4, 2, -6, -4, 0, 6, 0, -2, 4, 0, -2, 8, 12, 6, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 203280, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '203280.de', 'trace_hash': 706110417582586669}
• 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': '0.0023461209804170927676387275731', 'prec': 110}, 'conductor': 203280, 'gens': [[3304, 9680, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6255767748537774471980372644', 'prec': 100}], 'lmfdb_label': '203280.de5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14606911694160930223728544099', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6987175365683323282277491878205195926', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[3128, 0, 1], [3249, 0, 1]], 'xcoord_integral_points': [-6376, -3406, 3074, 3128, 3249, 3304, 6849, 24424]}
• lmfdb_label 203280.de5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8900411
    {'degree': 2, 'field': [-96, -1, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 4]}
  • id: 8900412
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 6]}
  • id: 8900415
    {'degree': 4, 'field': [36, 0, -23, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 12]}
  • id: 8900414
    {'degree': 4, 'field': [1089, 0, 0, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 4]}
  • id: 8900413
    {'degree': 4, 'field': [4761, 0, -72, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 4]}
  • id: 8900416
    {'degree': 6, 'field': [17457, 0, -1397, 0, 11, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 6]}
  • id: 8900420
    {'degree': 8, 'field': [225, 180, -108, -156, 109, -40, 18, -4, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 12]}
  • id: 8900417
    {'degree': 8, 'field': [104976, 0, 0, 0, 4113, 0, 0, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [4, 4]}
  • id: 8900419
    {'degree': 8, 'field': [197785, 29680, -28706, -1964, 1023, -52, 22, -4, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 12]}
  • id: 8900418
    {'degree': 8, 'field': [567666, 276804, -22033, -45628, -6995, 348, 17, -4, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 8]}
  • id: 8900421
    {'degree': 12, 'field': [3236149, 6458298, 4858343, 1130184, -234486, -54978, 8683, -8316, 966, -66, 35, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [6, 6]}
  • id: 8900422
    {'degree': 12, 'field': [78021889, 0, -16704050, 0, 1102431, 0, -4444, 0, -1749, 0, 22, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 12]}
  • id: 8900425
    {'degree': 16, 'field': [30140100, 0, 29882520, 0, 1978416, 0, -2292732, 0, 543109, 0, -57776, 0, 3354, 0, -92, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [4, 12]}
  • id: 8900426
    {'degree': 16, 'field': [8852928100, 0, -15571501600, 0, 3411421020, 0, 41468140, 0, -7056539, 0, -63266, 0, 2331, 0, -46, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 24]}
  • id: 8900424
    {'degree': 16, 'field': [11019960576, 0, 0, 0, 122192064, 0, 0, 0, 890820, 0, 0, 0, 1164, 0, 0, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 8]}
  • id: 8900423
    {'degree': 16, 'field': [34014848450625, 0, -9405879084000, 0, 1136691435600, 0, 28610562960, 0, 606668706, 0, 5404896, 0, 47376, 0, 336, 0, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 8]}
  • id: 8900427
    {'degree': 18, 'field': [97680263487425, 9923420659800, 857672660865, -179186429738, -1260835916163, 25159755942, -30683183386, 2233147026, 1050746049, 67597190, 3897270, 845130, -453665, -15822, 11778, 478, -174, -6, 1], 'lmfdb_label': '203280.de5', 'torsion': [2, 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: 5032331
    {'conductor': 203280, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '203280.de5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5032332
    {'conductor': 203280, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '203280.de5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5032333
    {'conductor': 203280, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '203280.de5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 5032334
    {'conductor': 203280, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '203280.de5', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5032335
    {'conductor': 203280, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '203280.de5', 'prime': 11, 'reduction_type': 0, '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: 2965400
    {'adelic_gens': [[9229, 12, 9228, 13], [4621, 12, 6, 73], [833, 9234, 5886, 5], [3081, 4, 7702, 9], [3697, 6, 0, 1], [2303, 9228, 4686, 113], [1, 12, 0, 1], [1, 0, 12, 1], [5281, 6, 0, 1], [9, 4, 9224, 9233]], 'adelic_image': '9240.384.5.?', 'conductor': 203280, 'lmfdb_label': '203280.de5', 'prime': 0}
  • id: 752189
    {'conductor': 203280, 'elladic_image': '4.12.0.1', 'lmfdb_label': '203280.de5', 'modell_image': '2Cs', 'prime': 2}
  • id: 752190
    {'conductor': 203280, 'elladic_image': '3.4.0.1', 'lmfdb_label': '203280.de5', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 203280.de does not appear in ec_padic