Elliptic curve data - 2850.p2

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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': '2850q', 'Clabel': '2850q4', 'Cnumber': 4, 'abc_quality': 1.0434886781558426, 'absD': 5158757273703750000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [1, 1, 1, -5844088, 4196148281], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 2850, 'degree': 215040, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8781260430338843857804627160', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [1412712966892699019449, 330160465517040000], 'lmfdb_iso': '2850.p', 'lmfdb_label': '2850.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -233764, 33569186], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '24.24.0-24.s.1.6', '40.24.0-40.bb.1.5', '60.12.0-4.c.1.1', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 75], [3, 4, 950], [5, 18, 38], [7, 2, 1425], [19, 20, 150]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.0734070868168341984800830494', 'prec': 100}, 'szpiro_ratio': 7.335748777269426, '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, 0, -1, -4, 1, 1, 0, 0, -1, -2, -4, 0, 1, 2, 1, -1, 0], 'aplist': [1, -1, 0, -4, 0, -2, 2, -1, 0, 10, 0, -2, 2, 4, 0, 6, 8, 6, -12, 0, 14, 0, 12, 10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 2850, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '2850.p', 'trace_hash': 235806217216184862}
• 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': '0.0031629438527912265960603395176', 'prec': 110}, 'conductor': 2850, 'gens': [], 'heights': [], 'lmfdb_label': '2850.p2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.12813413231169064976107934771', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7938778523636690966551108678696804130', 'prec': 130}, 'tamagawa_product': 56, 'torsion_generators': [[7635, -7639, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [0, 0], '5': 'a', '7': [2, 0], '19': [0, 0]}, 'iwp0': 11, 'lmfdb_label': '2850.p2'}
• ec_torsion_growth •

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

  
  
  • id: 148099
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [4]}
  • id: 148098
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [4]}
  • id: 148097
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [2, 2]}
  • id: 148100
    {'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [2, 4]}
  • id: 148101
    {'degree': 4, 'field': [6, 0, -8, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [8]}
  • id: 148105
    {'degree': 8, 'field': [-1504, -896, 752, 287, -140, -7, 7, -4, 1], 'lmfdb_label': '2850.p2', 'torsion': [6]}
  • id: 148104
    {'degree': 8, 'field': [1, 0, -20, 0, 48, 0, -20, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [2, 8]}
  • id: 148103
    {'degree': 8, 'field': [1, 2, 2, 14, 34, -14, 2, -2, 1], 'lmfdb_label': '2850.p2', 'torsion': [8]}
  • id: 148102
    {'degree': 8, 'field': [460, 720, 424, 192, 24, -24, 4, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [2, 4]}
  • id: 148107
    {'degree': 16, 'field': [1, 0, 0, 0, 1, 0, 0, 0, 96, 0, 0, 0, 1, 0, 0, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [2, 8]}
  • id: 148106
    {'degree': 16, 'field': [100, 0, 0, -960, 29164, 16272, 4608, -2112, 1149, 696, 288, -144, -38, -24, 0, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [4, 4]}
  • id: 148109
    {'degree': 16, 'field': [97576, 101344, -2654052, 9199008, -14414034, 10615584, -1639295, -1555496, 302604, 51258, -4635, -2268, -259, 266, -18, -8, 1], 'lmfdb_label': '2850.p2', 'torsion': [2, 6]}
  • id: 148110
    {'degree': 16, 'field': [200704, 0, -4370432, 0, -650240, 0, -161184, 0, -15840, 0, 24, 0, 388, 0, -20, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [12]}
  • id: 148111
    {'degree': 16, 'field': [26132544, 0, -7706448, 0, 496620, 0, -817911, 0, 170010, 0, -519, 0, 333, 0, -30, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [12]}
  • id: 148108
    {'degree': 16, 'field': [443523600, 0, -755049600, 0, 398652480, 0, -61021440, 0, -1893474, 0, 234576, 0, 8936, 0, -64, 0, 1], 'lmfdb_label': '2850.p2', 'torsion': [16]}
• 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: 50686
    {'conductor': 2850, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '2850.p2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 50687
    {'conductor': 2850, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '2850.p2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 50688
    {'conductor': 2850, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '2850.p2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 50689
    {'conductor': 2850, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '2850.p2', 'prime': 19, '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: 1682577
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [44, 1, 103, 6], [113, 8, 112, 9], [7, 6, 114, 115], [1, 4, 4, 17], [23, 112, 92, 87], [48, 113, 73, 0], [16, 83, 49, 78]], 'adelic_image': '120.48.0.?', 'conductor': 2850, 'lmfdb_label': '2850.p2', 'prime': 0}
  • id: 14244
    {'conductor': 2850, 'elladic_image': '8.12.0.6', 'lmfdb_label': '2850.p2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 2850.p does not appear in ec_padic