Elliptic curve data - 55770.by3

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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': '55770bq', 'Clabel': '55770bq1', 'Cnumber': 1, 'abc_quality': 0.9075122139890862, 'absD': 1019422060800, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3432, 'ainvs': [1, 1, 1, -3806, -77797], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 55770, 'degree': 147456, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0253208942859168267761270146', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 50, 'isogeny_degrees': [1, 2, 4], 'jinv': [1263214441, 211200], 'lmfdb_iso': '55770.by', 'lmfdb_label': '55770.by3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -22, -44], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '66.6.0.a.1', '88.12.0.?', '104.12.0.?', '132.12.0.?', '156.12.0.?', '264.24.0.?', '312.24.0.?', '572.12.0.?', '1144.24.0.?', '1716.24.0.?', '3432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 5577], [3, 4, 18590], [5, 6, 11154], [11, 12, 5070], [13, 86, 330]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.25715378444485154125061670618', 'prec': 107}, 'szpiro_ratio': 3.325706862529695, '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, 1, -1, 1, -1, -1, 4, 1, 1, -1, -1, -1, 0, 4, 1, 1, -2, 1, 8, -1], 'aplist': [1, -1, -1, 4, -1, 0, -2, 8, 0, 2, 8, 10, 10, 0, 0, 14, 4, 14, 4, -8, -10, 12, -4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 55770, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '55770.by', 'trace_hash': 1893902019854083547}
• 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': '0.12865230950468977162598874041', 'prec': 103}, 'conductor': 55770, 'gens': [], 'heights': [], 'lmfdb_label': '55770.by3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.61473845022644853243538640536', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9179076018115882594830912429124278205', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-47, 23, 1]], 'xcoord_integral_points': [-47]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [0, 0], '5': [0, 0], '11': [0, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '55770.by3'}
• ec_torsion_growth •

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

  
  
  • id: 2695611
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '55770.by3', 'torsion': [2, 2]}
  • id: 2695613
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '55770.by3', 'torsion': [4]}
  • id: 2695612
    {'degree': 2, 'field': [36, -1, 1], 'lmfdb_label': '55770.by3', 'torsion': [4]}
  • id: 2695614
    {'degree': 4, 'field': [108, -63, 19, -1, 1], 'lmfdb_label': '55770.by3', 'torsion': [2, 4]}
  • id: 2695618
    {'degree': 8, 'field': [-137920, 153248, 52016, 5396, 20, -424, 1, -2, 1], 'lmfdb_label': '55770.by3', 'torsion': [6]}
  • id: 2695616
    {'degree': 8, 'field': [92, 34, 83, -94, 72, 20, -14, -2, 1], 'lmfdb_label': '55770.by3', 'torsion': [8]}
  • id: 2695617
    {'degree': 8, 'field': [16384, 3328, 350, 658, 577, 38, -28, -4, 1], 'lmfdb_label': '55770.by3', 'torsion': [8]}
  • id: 2695615
    {'degree': 8, 'field': [568096, -197008, -61102, 5390, 1981, 220, -52, -2, 1], 'lmfdb_label': '55770.by3', 'torsion': [2, 4]}
  • id: 2695620
    {'degree': 16, 'field': [8464, 3128, -6480, 20118, 3461, -10858, -396, -10748, 7998, -1324, 1386, -86, 164, -12, 18, -2, 1], 'lmfdb_label': '55770.by3', 'torsion': [2, 8]}
  • id: 2695621
    {'degree': 16, 'field': [27971584, 25947136, 24591488, 11727744, 5866040, 2075096, 883018, 207186, 17977, -25158, -7088, 634, 902, 54, -34, -4, 1], 'lmfdb_label': '55770.by3', 'torsion': [2, 8]}
  • id: 2695624
    {'degree': 16, 'field': [3929033124, 0, 850994712, 0, 75017268, 0, 7675635, 0, 524058, 0, 24051, 0, 1273, 0, 26, 0, 1], 'lmfdb_label': '55770.by3', 'torsion': [12]}
  • id: 2695622
    {'degree': 16, 'field': [72770457600, 0, -63319219200, 0, -3449692160, 0, 9724272, 0, 11357232, 0, -135832, 0, 249, 0, -66, 0, 1], 'lmfdb_label': '55770.by3', 'torsion': [2, 6]}
  • id: 2695623
    {'degree': 16, 'field': [192885349904, -39495147640, 43131561372, -7461626914, 4207884896, -586656498, 219067543, -19940672, 4692984, 230510, -81775, 19380, -3139, -70, 30, -8, 1], 'lmfdb_label': '55770.by3', 'torsion': [12]}
  • id: 2695619
    {'degree': 16, 'field': [322733065216, 0, 108235755648, 0, 8107996996, 0, 243536688, 0, 8255529, 0, 355068, 0, 7546, 0, 108, 0, 1], 'lmfdb_label': '55770.by3', 'torsion': [4, 4]}
• 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: 1341888
    {'conductor': 55770, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '55770.by3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1341889
    {'conductor': 55770, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '55770.by3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1341890
    {'conductor': 55770, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '55770.by3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1341891
    {'conductor': 55770, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '55770.by3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1341892
    {'conductor': 55770, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '55770.by3', 'prime': 13, '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: 2034875
    {'adelic_gens': [[976, 2379, 2821, 794], [7, 6, 3426, 3427], [791, 0, 0, 3431], [2692, 793, 2015, 534], [3425, 8, 3424, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [235, 234, 442, 2419], [2809, 2808, 2158, 703]], 'adelic_image': '3432.48.0.?', 'conductor': 55770, 'lmfdb_label': '55770.by3', 'prime': 0}
  • id: 237688
    {'conductor': 55770, 'elladic_image': '4.6.0.1', 'lmfdb_label': '55770.by3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 55770.by does not appear in ec_padic