Elliptic curve data - 7200.u1

Formats: - HTML - YAML - JSON - 2024-04-27T21:48:41.858045

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '7200h', 'Clabel': '7200h2', 'Cnumber': 2, 'abc_quality': 1.0033704496961282, 'absD': 699840000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 0, 0, -18300, -952000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 7200, 'degree': 12288, 'elladic_images': ['8.12.0.13'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1907572354680081286998196273', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 4], 'jinv': [14526784, 15], 'lmfdb_iso': '7200.u', 'lmfdb_label': '7200.u1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -81, -255], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.6', '12.12.0-4.c.1.2', '20.12.0-4.c.1.1', '24.24.0-24.bb.1.15', '40.24.0-40.bb.1.16', '60.24.0-60.h.1.2', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.85641504564304221371541477923', 'prec': 107}, 'szpiro_ratio': 4.622644534225408, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 8, 0], 'aplist': [0, 0, 0, 0, -4, -2, -2, 8, 4, 6, 0, -2, 6, -4, -12, -6, -12, 14, 12, 0, -2, -8, -4, -2, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 7200, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '7200.u', 'trace_hash': 71747468733612620}
• 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': '0.092410518435061976945203377774', 'prec': 107}, 'conductor': 7200, 'gens': [], 'heights': [], 'lmfdb_label': '7200.u1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.41050051504809980288817835679', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6420020601923992115527134271627198446', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-80, 0, 1]], 'xcoord_integral_points': [-80]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a'}, 'iwp0': 3, 'lmfdb_label': '7200.u1'}
• ec_torsion_growth •

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

  
  
  • id: 378562
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '7200.u1', 'torsion': [2, 2]}
  • id: 378564
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '7200.u1', 'torsion': [4]}
  • id: 378563
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '7200.u1', 'torsion': [4]}
  • id: 378565
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '7200.u1', 'torsion': [2, 4]}
  • id: 378569
    {'degree': 8, 'field': [-675, 0, -480, 0, -90, 0, 0, 0, 1], 'lmfdb_label': '7200.u1', 'torsion': [6]}
  • id: 378566
    {'degree': 8, 'field': [121, 244, -268, 52, -35, 8, 2, -4, 1], 'lmfdb_label': '7200.u1', 'torsion': [2, 4]}
  • id: 378567
    {'degree': 8, 'field': [150, 240, 36, -168, -50, 32, 12, -4, 1], 'lmfdb_label': '7200.u1', 'torsion': [8]}
  • id: 378568
    {'degree': 8, 'field': [225, 0, -150, 0, 85, 0, -10, 0, 1], 'lmfdb_label': '7200.u1', 'torsion': [8]}
  • id: 378573
    {'degree': 16, 'field': [-51815, 429160, -1164516, 1502356, -1010318, 260832, 87656, -66988, -5097, 14456, -3184, -492, 154, 16, 12, -8, 1], 'lmfdb_label': '7200.u1', 'torsion': [2, 6]}
  • id: 378575
    {'degree': 16, 'field': [1, -4, 12, 56, -158, 60, 1040, -812, -381, -812, 1040, 60, -158, 56, 12, -4, 1], 'lmfdb_label': '7200.u1', 'torsion': [12]}
  • id: 378571
    {'degree': 16, 'field': [601, -4684, 17596, -41476, 69308, -87664, 87504, -70108, 46253, -24944, 11316, -4148, 1298, -308, 64, -8, 1], 'lmfdb_label': '7200.u1', 'torsion': [2, 8]}
  • id: 378572
    {'degree': 16, 'field': [2281, -15200, 47616, -90964, 115758, -101028, 59560, -21592, 3141, 532, 148, -360, 108, 4, 0, -4, 1], 'lmfdb_label': '7200.u1', 'torsion': [2, 8]}
  • id: 378574
    {'degree': 16, 'field': [8100, 0, 71280, 0, 211356, 0, 25116, 0, 2505, 0, 240, 0, -50, 0, -4, 0, 1], 'lmfdb_label': '7200.u1', 'torsion': [12]}
  • id: 378570
    {'degree': 16, 'field': [58081, 0, -52252, 0, 39118, 0, -12484, 0, 235, 0, -4, 0, 58, 0, 8, 0, 1], 'lmfdb_label': '7200.u1', '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: 147948
    {'conductor': 7200, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '7200.u1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 147949
    {'conductor': 7200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '7200.u1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 147950
    {'conductor': 7200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '7200.u1', 'prime': 5, '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: 1711694
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [113, 8, 112, 9], [92, 119, 49, 114], [83, 78, 50, 107], [7, 6, 114, 115], [1, 4, 4, 17], [32, 117, 35, 118], [16, 83, 19, 48]], 'adelic_image': '120.48.0.?', 'conductor': 7200, 'lmfdb_label': '7200.u1', 'prime': 0}
  • id: 35608
    {'conductor': 7200, 'elladic_image': '8.12.0.13', 'lmfdb_label': '7200.u1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 7200.u does not appear in ec_padic