Elliptic curve data - 4025.e4

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

  
  {'Ciso': '4025a', 'Clabel': '4025a4', 'Cnumber': 4, 'abc_quality': 0.9793224770887127, 'absD': 30607609375, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 6440, 'ainvs': [1, -1, 0, 658, 5191], 'analytic_rank': 0, 'bad_primes': [5, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4025, 'degree': 2560, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.69908510902360492517159946386', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [2014698447, 1958887], 'lmfdb_iso': '4025.e', 'lmfdb_label': '4025.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, 26, 36], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '14.6.0.b.1', '20.12.0-4.c.1.1', '28.12.0.g.1', '140.24.0.?', '184.12.0.?', '920.24.0.?', '1288.24.0.?', '6440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.10563384719344526212878020275', 'prec': 107}, 'szpiro_ratio': 3.7444956231300157, '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, -1, -3, -3, 0, 4, 0, -6, -1, 0, -1, 2, -3, 4, 0], 'aplist': [1, 0, 0, -1, 4, -6, 2, 4, 1, -2, -4, 2, -6, -12, 12, 10, 0, 2, -12, 8, 14, 8, 4, 6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 4025, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '4025.e', 'trace_hash': 440634469277035009}
• 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': '0.24704859568363602051016381465', 'prec': 103}, 'conductor': 4025, 'gens': [], 'heights': [], 'lmfdb_label': '4025.e4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.77174248321588238645404284847', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5434849664317647729080856969377655934', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-29, 29, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '5': 'a', '7': [0, 0], '23': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4025.e4'}
• ec_torsion_growth •

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

  
  
  • id: 209081
    {'degree': 2, 'field': [-35, 0, 1], 'lmfdb_label': '4025.e4', 'torsion': [4]}
  • id: 209080
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '4025.e4', 'torsion': [2, 2]}
  • id: 209082
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '4025.e4', 'torsion': [4]}
  • id: 209083
    {'degree': 4, 'field': [14, -14, 15, -2, 1], 'lmfdb_label': '4025.e4', 'torsion': [2, 4]}
  • id: 209084
    {'degree': 8, 'field': [4, 8, 2, -4, 11, -13, 8, -1, 1], 'lmfdb_label': '4025.e4', 'torsion': [2, 4]}
  • id: 209085
    {'degree': 8, 'field': [784, 0, 2352, 0, -3927, 0, -84, 0, 1], 'lmfdb_label': '4025.e4', 'torsion': [8]}
  • id: 209087
    {'degree': 8, 'field': [1059, -1806, 699, -441, 240, -42, 21, 0, 1], 'lmfdb_label': '4025.e4', 'torsion': [6]}
  • id: 209086
    {'degree': 8, 'field': [3364, 0, 2072, 0, 120, 0, 4, 0, 1], 'lmfdb_label': '4025.e4', 'torsion': [8]}
  • id: 209092
    {'degree': 16, 'field': [-350451, -808542, 3715029, -6003144, 5186862, -1780002, -213273, 680526, -107421, 42336, 7782, -2436, 564, -84, 42, 0, 1], 'lmfdb_label': '4025.e4', 'torsion': [12]}
  • id: 209088
    {'degree': 16, 'field': [1, 2, 2, -20, 21, -44, 70, -22, -44, 22, 70, 44, 21, 20, 2, -2, 1], 'lmfdb_label': '4025.e4', 'torsion': [4, 4]}
  • id: 209093
    {'degree': 16, 'field': [124609, 0, 156313, 0, 58828, 0, -13391, 0, -6335, 0, 679, 0, 7, 0, 10, 0, 1], 'lmfdb_label': '4025.e4', 'torsion': [12]}
  • id: 209091
    {'degree': 16, 'field': [170011, -150315, 766469, -1394595, 1287169, -844380, 295202, -30960, -113, 3015, 611, -570, 256, -60, 8, 0, 1], 'lmfdb_label': '4025.e4', 'torsion': [2, 6]}
  • id: 209090
    {'degree': 16, 'field': [2189761, -2709308, 4069422, -3022628, 2292404, -1010300, 467294, -131732, 62637, -27796, 14258, -5660, 1732, -392, 76, -8, 1], 'lmfdb_label': '4025.e4', 'torsion': [2, 8]}
  • id: 209089
    {'degree': 16, 'field': [328030304, -302291584, 283289776, 37861712, -17894436, -3219272, 4570412, -3419640, 1410865, -415920, 130088, -27664, 6370, -840, 140, -8, 1], 'lmfdb_label': '4025.e4', '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: 75136
    {'conductor': 4025, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4025.e4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 75137
    {'conductor': 4025, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4025.e4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 75138
    {'conductor': 4025, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '4025.e4', 'prime': 23, 'reduction_type': 1, '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: 1690092
    {'adelic_gens': [[1131, 1130, 5970, 171], [281, 5160, 3700, 1321], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [4056, 5155, 925, 3866], [3863, 0, 0, 6439], [6433, 8, 6432, 9], [7, 6, 6434, 6435], [491, 3060, 530, 2421]], 'adelic_image': '6440.48.0.?', 'conductor': 4025, 'lmfdb_label': '4025.e4', 'prime': 0}
  • id: 19893
    {'conductor': 4025, 'elladic_image': '4.6.0.1', 'lmfdb_label': '4025.e4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4025.e does not appear in ec_padic