Elliptic curve data - 242550.mm2

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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': '242550mm', 'Clabel': '242550mm3', 'Cnumber': 3, 'abc_quality': 0.990076389601979, 'absD': 1934320849590937500, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 18480, 'ainvs': [1, -1, 1, -12954605, 17949803897], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 242550, 'degree': 9437184, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6804952252811926635282572462', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 324, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [179415687049201, 1443420], 'lmfdb_iso': '242550.mm', 'lmfdb_label': '242550.mm2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1175, 15405], 'min_quad_twist_disc': 105, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '40.24.0.cb.1', '48.24.0.h.1', '88.24.0.?', '112.24.0.?', '168.24.0.?', '220.12.0.?', '240.48.0.?', '336.48.0.?', '420.12.0.?', '440.48.0.?', '528.48.0.?', '560.48.0.?', '840.48.0.?', '924.12.0.?', '1232.48.0.?', '1680.96.0.?', '1848.48.0.?', '2640.96.1.?', '3696.96.0.?', '4620.24.0.?', '6160.96.0.?', '9240.96.0.?', '18480.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.3863180347705426505909247708', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 121275], [3, 8, 26950], [5, 18, 9702], [7, 26, 4950], [11, 12, 22050]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.35351505020243097797757858940', 'prec': 103}, 'szpiro_ratio': 4.899158732190039, '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, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 1, -2, 0, 4, 0], 'aplist': [1, 0, 0, 0, 1, -2, -2, 4, 0, 2, 0, 2, 2, 12, -8, 6, -12, -6, -4, 0, -6, -16, -4, 10, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 242550, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '242550.mm', 'trace_hash': 1503710661536791600}
• 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': '0.0046962523975006231516923956138', 'prec': 110}, 'conductor': 242550, 'gens': [[2095, 226, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.3863180347705426505909247708', 'prec': 100}], 'lmfdb_label': '242550.mm2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.23605744275111638105826407290', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.789849210078724839033221308613277267', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[8331, -8335, 2]], 'xcoord_integral_points': [2095, 6639]}
• lmfdb_label 242550.mm2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10464951
    {'degree': 2, 'field': [-231, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [4]}
  • id: 10464949
    {'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [2, 2]}
  • id: 10464950
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '242550.mm2', 'torsion': [4]}
  • id: 10464953
    {'degree': 4, 'field': [-6, 96, -95, -2, 1], 'lmfdb_label': '242550.mm2', 'torsion': [8]}
  • id: 10464954
    {'degree': 4, 'field': [64, 0, -26, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [8]}
  • id: 10464952
    {'degree': 4, 'field': [1936, 0, -143, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [2, 4]}
  • id: 10464958
    {'degree': 8, 'field': [-4562144, 484256, 161992, -38732, 1580, 757, -83, -1, 1], 'lmfdb_label': '242550.mm2', 'torsion': [6]}
  • id: 10464957
    {'degree': 8, 'field': [38025, 0, -16680, 0, 2314, 0, -104, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [2, 8]}
  • id: 10464955
    {'degree': 8, 'field': [475476, -78756, 82942, -8478, 4505, -322, 112, -4, 1], 'lmfdb_label': '242550.mm2', 'torsion': [2, 4]}
  • id: 10464956
    {'degree': 8, 'field': [86397025, 0, 0, 0, -4510, 0, 0, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [8]}
  • id: 10464964
    {'degree': 16, 'field': [-7617166749, -3196088901, 2262039804, 1271098683, 80185716, 67966857, 6365494, -12714467, -3032904, 353397, 134376, -1779, 1104, -537, 6, -5, 1], 'lmfdb_label': '242550.mm2', 'torsion': [12]}
  • id: 10464961
    {'degree': 16, 'field': [914177664, -60217344, -2620349568, 702991872, 1852487280, -370465920, -515697264, 41798592, 49872268, -2163216, -2031016, 43296, 38508, -264, -328, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [16]}
  • id: 10464962
    {'degree': 16, 'field': [4038309136, 1383851456, -1162743024, -421150256, 159268578, 57824256, -13225976, -4810928, 751983, 275456, -30944, -12048, 1098, 392, -36, -8, 1], 'lmfdb_label': '242550.mm2', 'torsion': [16]}
  • id: 10464959
    {'degree': 16, 'field': [32907774025, 0, 11282090400, 0, 1339754810, 0, 76218660, 0, 3995331, 0, 143676, 0, 3866, 0, 36, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [4, 4]}
  • id: 10464960
    {'degree': 16, 'field': [588083461956, 0, 70205016648, 0, -11220878432, 0, 184160516, 0, 58581285, 0, 30196, 0, -15042, 0, 8, 0, 1], 'lmfdb_label': '242550.mm2', 'torsion': [2, 8]}
  • id: 10464963
    {'degree': 16, 'field': [5265499764816, 634688698752, -566753137440, 92645406480, 4451157300, -22386030324, -1799613123, 277844490, -5529755, 11238700, -479138, -294616, 30590, 2120, -275, -2, 1], 'lmfdb_label': '242550.mm2', 'torsion': [2, 6]}
  • id: 10464965
    {'degree': 16, 'field': [135877629102336, 0, -17128721884032, 0, 975508897968, 0, -33853428279, 0, 755428410, 0, -10745559, 0, 93753, 0, -462, 0, 1], 'lmfdb_label': '242550.mm2', '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: 6012093
    {'conductor': 242550, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '242550.mm2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6012094
    {'conductor': 242550, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '242550.mm2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6012095
    {'conductor': 242550, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '242550.mm2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6012096
    {'conductor': 242550, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '242550.mm2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6012097
    {'conductor': 242550, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '242550.mm2', 'prime': 11, '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: 3205631
    {'adelic_gens': [[5293, 13216, 924, 8905], [1, 16, 0, 1], [18465, 16, 18464, 17], [16178, 4627, 10255, 9262], [12319, 5264, 8792, 5151], [13199, 0, 0, 18479], [15, 2, 18382, 18467], [7384, 2639, 8897, 5270], [5, 4, 18476, 18477], [1, 0, 16, 1], [736, 5285, 14595, 2626]], 'adelic_image': '18480.192.1.?', 'conductor': 242550, 'lmfdb_label': '242550.mm2', 'prime': 0}
  • id: 878277
    {'conductor': 242550, 'elladic_image': '8.12.0.5', 'lmfdb_label': '242550.mm2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 242550.mm does not appear in ec_padic