Elliptic curve data - 48552.f2

Formats: - HTML - YAML - JSON - 2025-09-22T13:56:12.910485

• 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': '48552i', 'Clabel': '48552i2', 'Cnumber': 2, 'abc_quality': 0.9539300254639066, 'absD': 2725034989824, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1428, 'ainvs': [0, -1, 0, -3564, 21204], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 48552, 'degree': 73728, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0769920768172299289171015779', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [810448, 441], 'lmfdb_iso': '48552.f', 'lmfdb_label': '48552.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -12, 0], 'min_quad_twist_disc': 17, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0.b.1', '28.12.0.a.1', '68.12.0-2.a.1.1', '84.24.0.?', '204.24.0.?', '476.24.0.?', '1428.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 289], [3, 4, 16184], [7, 8, 6936], [17, 146, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.80171271558417498415248714534', 'prec': 107}, 'szpiro_ratio': 3.3501845376013812, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, -2, 0, 1, 0, 1, 0, 0, 0, -2, 0, 2, 0, 0, 0, -4, 0], 'aplist': [0, -1, -2, 1, 0, -2, 0, -4, 4, -6, 8, 10, 10, 12, -8, 6, 4, 10, 12, -4, -2, -8, 4, 6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 48552, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '48552.f', 'trace_hash': 899778262317377911}
• 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': '0.11602099027086435892791711739', 'prec': 103}, 'conductor': 48552, 'gens': [], 'heights': [], 'lmfdb_label': '48552.f2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.70396565221983250833393824761', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4079313044396650166678764952265599770', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[6, 0, 1], [57, 0, 1]], 'xcoord_integral_points': [-62, 6, 57]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': [1, 0], '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '48552.f2'}
• ec_torsion_growth •

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

  
  
  • id: 2364189
    {'degree': 4, 'field': [16, 4, 5, -1, 1], 'lmfdb_label': '48552.f2', 'torsion': [2, 4]}
  • id: 2364190
    {'degree': 4, 'field': [36, 0, 5, 0, 1], 'lmfdb_label': '48552.f2', 'torsion': [2, 4]}
  • id: 2364191
    {'degree': 4, 'field': [289, 0, -85, 0, 1], 'lmfdb_label': '48552.f2', 'torsion': [2, 4]}
  • id: 2364192
    {'degree': 8, 'field': [-320254, 159868, -90442, 12218, -3098, 44, 16, -4, 1], 'lmfdb_label': '48552.f2', 'torsion': [2, 6]}
  • id: 2364193
    {'degree': 16, 'field': [71824, 0, 79084, 0, 32129, 0, 20988, 0, 19172, 0, 5394, 0, 668, 0, 40, 0, 1], 'lmfdb_label': '48552.f2', 'torsion': [4, 4]}
  • id: 2364194
    {'degree': 16, 'field': [123877, -63628, 21978, 100636, -76716, -10932, 60826, -23348, -21867, 11972, 3550, -2556, -120, 224, -12, -8, 1], 'lmfdb_label': '48552.f2', 'torsion': [2, 8]}
  • id: 2364195
    {'degree': 16, 'field': [1830969, -1173018, 2364124, -1615894, 1432810, -729780, 411882, -152586, 59967, -14508, 4182, -618, 234, -42, 22, -4, 1], 'lmfdb_label': '48552.f2', 'torsion': [2, 8]}
  • id: 2364196
    {'degree': 16, 'field': [1997374864, 0, -468987104, 0, 1529104, 0, -9782720, 0, 528940, 0, -7376, 0, 5620, 0, -152, 0, 1], 'lmfdb_label': '48552.f2', 'torsion': [2, 8]}
• 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: 1160217
    {'conductor': 48552, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '48552.f2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1160218
    {'conductor': 48552, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '48552.f2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1160219
    {'conductor': 48552, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '48552.f2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1160220
    {'conductor': 48552, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48552.f2', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1987344
    {'adelic_gens': [[1, 0, 4, 1], [409, 170, 0, 1], [1, 4, 0, 1], [171, 170, 782, 1259], [167, 0, 0, 1427], [885, 340, 680, 851], [1425, 4, 1424, 5]], 'adelic_image': '1428.48.0.?', 'conductor': 48552, 'lmfdb_label': '48552.f2', 'prime': 0}
  • id: 209383
    {'conductor': 48552, 'elladic_image': '2.6.0.1', 'lmfdb_label': '48552.f2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 48552.f does not appear in ec_padic