Elliptic curve data - 12870.m3

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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': '12870t', 'Clabel': '12870t1', 'Cnumber': 1, 'abc_quality': 0.8577893570160732, 'absD': 6404935680, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 17160, 'ainvs': [1, -1, 0, -594, 4180], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 12870, 'degree': 9216, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.58916446416692527981031125818', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4], 'jinv': [31824875809, 8785920], 'lmfdb_iso': '12870.m', 'lmfdb_label': '12870.m3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -66, -177], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0-4.c.1.2', '24.12.0-4.c.1.6', '120.24.0.?', '1144.12.0.?', '1716.12.0.?', '3432.24.0.?', '4290.6.0.?', '5720.24.0.?', '8580.24.0.?', '17160.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.4200602891105349085698020590', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 6435], [3, 8, 715], [5, 6, 2574], [11, 12, 1170], [13, 14, 990]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.039858319832870434112688639719', 'prec': 107}, 'szpiro_ratio': 3.2522785714746036, '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, 0, 1, 1, 0, -4, -1, 0, -1, -1, 0, -1, 4, 0, 1, -2, 0, 4, 1], 'aplist': [-1, 0, 1, -4, -1, -1, -2, 4, 0, -2, 8, -6, 6, -4, 0, 2, 12, 2, -12, 0, -14, 0, -4, 10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 12870, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '12870.m', 'trace_hash': 1546496561122679230}
• 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': '0.30779265266884517735298377717', 'prec': 103}, 'conductor': 12870, 'gens': [[29, 89, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.4200602891105349085698020590', 'prec': 100}], 'lmfdb_label': '12870.m3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.2472669315106113456931837119', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0184611708695798360615880710777401004', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[20, -10, 1]], 'xcoord_integral_points': [20, 29, 84]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [4, 0], '7': [1, 0], '11': [3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '12870.m3'}
• ec_torsion_growth •

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

  
  
  • id: 663395
    {'degree': 2, 'field': [-536, -1, 1], 'lmfdb_label': '12870.m3', 'torsion': [2, 2]}
  • id: 663396
    {'degree': 2, 'field': [-107, -1, 1], 'lmfdb_label': '12870.m3', 'torsion': [4]}
  • id: 663397
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '12870.m3', 'torsion': [4]}
  • id: 663398
    {'degree': 4, 'field': [11236, 0, -217, 0, 1], 'lmfdb_label': '12870.m3', 'torsion': [2, 4]}
  • id: 663402
    {'degree': 8, 'field': [-3888, 0, -2133, 0, -216, 0, 0, 0, 1], 'lmfdb_label': '12870.m3', 'torsion': [6]}
  • id: 663400
    {'degree': 8, 'field': [104976, 0, -204432, 0, 21964, 0, -292, 0, 1], 'lmfdb_label': '12870.m3', 'torsion': [8]}
  • id: 663401
    {'degree': 8, 'field': [266256, 0, 7056, 0, 1356, 0, 36, 0, 1], 'lmfdb_label': '12870.m3', 'torsion': [8]}
  • id: 663399
    {'degree': 8, 'field': [371718400, 0, 1158800, 0, -38460, 0, 20, 0, 1], 'lmfdb_label': '12870.m3', 'torsion': [2, 4]}
  • id: 663405
    {'degree': 16, 'field': [-632171349, 1627101504, 3437776890, -8585234160, 581040154, 4039721364, -671432358, -548633680, 100096211, 23916044, -3997558, -420352, 63264, 3108, -424, -8, 1], 'lmfdb_label': '12870.m3', 'torsion': [2, 8]}
  • id: 663408
    {'degree': 16, 'field': [158356, 136220, 5849, -401386, 280254, -69718, 61989, -69874, 29131, -3194, 1761, -1814, 231, 106, -4, -8, 1], 'lmfdb_label': '12870.m3', 'torsion': [12]}
  • id: 663407
    {'degree': 16, 'field': [879241104, 0, 216958692, 0, -153779375, 0, 17829204, 0, -425220, 0, -24754, 0, 348, 0, 0, 0, 1], 'lmfdb_label': '12870.m3', 'torsion': [12]}
  • id: 663404
    {'degree': 16, 'field': [10041783775, -2969606400, 3817224950, -1765429600, 1063861610, -233348820, 104740430, -23808240, 6895171, -732588, 252958, -61376, 13020, -1316, 208, -8, 1], 'lmfdb_label': '12870.m3', 'torsion': [2, 8]}
  • id: 663406
    {'degree': 16, 'field': [230400000000, 0, 190140000000, 0, -10760000000, 0, 950700000, 0, 4800000, 0, -396125, 0, -4800, 0, 0, 0, 1], 'lmfdb_label': '12870.m3', 'torsion': [2, 6]}
  • id: 663403
    {'degree': 16, 'field': [542437189058961, 0, 2701019115972, 0, 457096482018, 0, 933309684, 0, 138680035, 0, 38524, 0, 19338, 0, -8, 0, 1], 'lmfdb_label': '12870.m3', '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: 279120
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '12870.m3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 279121
    {'conductor': 12870, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '12870.m3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 279122
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12870.m3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 279123
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12870.m3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 279124
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12870.m3', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1749404
    {'adelic_gens': [[2153, 2148, 2150, 10727], [10564, 1, 9263, 6], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [13736, 3, 5, 2], [14044, 1, 7823, 6], [11432, 17157, 11435, 17158], [6443, 6438, 10730, 2147], [17153, 8, 17152, 9], [7, 6, 17154, 17155]], 'adelic_image': '17160.48.0.?', 'conductor': 12870, 'lmfdb_label': '12870.m3', 'prime': 0}
  • id: 61168
    {'conductor': 12870, 'elladic_image': '4.6.0.1', 'lmfdb_label': '12870.m3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 564987
    {'lmfdb_iso': '12870.m', 'p': 7, 'prec': 20, 'unit': 9456220637103726, 'val': 1}
  • id: 564991
    {'lmfdb_iso': '12870.m', 'p': 17, 'prec': 20, 'unit': 211004411739889723133308, 'val': 1}
  • id: 564983
    {'lmfdb_iso': '12870.m', 'p': 19, 'prec': 20, 'unit': 1613767306763185960329658, 'val': 1}
  • id: 564990
    {'lmfdb_iso': '12870.m', 'p': 29, 'prec': 20, 'unit': 5369689906372015428424859696, 'val': 1}
  • id: 564998
    {'lmfdb_iso': '12870.m', 'p': 31, 'prec': 20, 'unit': 13747716535776399577489039006, 'val': 1}
  • id: 564986
    {'lmfdb_iso': '12870.m', 'p': 37, 'prec': 20, 'unit': 68731255164439412065780691516, 'val': 1}
  • id: 564988
    {'lmfdb_iso': '12870.m', 'p': 41, 'prec': 20, 'unit': 2514184250055703321221739154782, 'val': 1}
  • id: 564989
    {'lmfdb_iso': '12870.m', 'p': 43, 'prec': 20, 'unit': 8588920171835434135840032770159, 'val': 1}
  • id: 564993
    {'lmfdb_iso': '12870.m', 'p': 53, 'prec': 20, 'unit': 532202302356371148196161894626247, 'val': 1}
  • id: 564996
    {'lmfdb_iso': '12870.m', 'p': 59, 'prec': 20, 'unit': 1306220108552330128197812058605633, 'val': 1}
  • id: 564997
    {'lmfdb_iso': '12870.m', 'p': 61, 'prec': 20, 'unit': 5415386472478641478077359195056341, 'val': 1}
  • id: 564985
    {'lmfdb_iso': '12870.m', 'p': 67, 'prec': 20, 'unit': 49083894817574190558360683516872855, 'val': 1}
  • id: 564994
    {'lmfdb_iso': '12870.m', 'p': 73, 'prec': 20, 'unit': 164692761496319951516208016138014913, 'val': 1}
  • id: 564992
    {'lmfdb_iso': '12870.m', 'p': 83, 'prec': 20, 'unit': 29220315210389575989395036764403092, 'val': 1}
  • id: 564995
    {'lmfdb_iso': '12870.m', 'p': 89, 'prec': 20, 'unit': 4617040672876757787177835175752369901, 'val': 1}
  • id: 564984
    {'lmfdb_iso': '12870.m', 'p': 97, 'prec': 20, 'unit': 14017776850949944510857327926765611507, 'val': 1}