Elliptic curve data - 4400.s2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4400v', 'Clabel': '4400v1', 'Cnumber': 1, 'abc_quality': 1.0648872065191846, 'absD': 11264000, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 2200, 'ainvs': [0, 1, 0, -448, 3508], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 4400, 'degree': 1152, 'elladic_images': ['25.60.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.26683732912770937591308982963', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 5, 25], 'jinv': [-19465109, 22], 'lmfdb_iso': '4400.s', 'lmfdb_label': '4400.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -28, -69], 'min_quad_twist_disc': -4, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '20.24.0-5.a.2.2', '25.60.0.a.2', '100.120.0.?', '275.300.12.?', '440.48.1.?', '1100.600.12.?', '2200.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.22035584825563752770771466299', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 55], [11, 12, 400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.82866932954076102715433212513', 'prec': 107}, 'szpiro_ratio': 3.567872378069047, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, -3, 0, -2, 0, -1, 0, 4, 0, 0, 0, 3, 0, 5, 0], 'aplist': [0, 1, 0, -3, -1, 4, 3, 5, -4, 5, -7, -7, -8, 6, -8, 9, 0, -13, 12, 3, -6, 0, -4, -15, -12], 'class_deg': 25, 'class_size': 3, 'conductor': 4400, 'isogeny_matrix': [[1, 25, 5], [25, 1, 5], [5, 5, 1]], 'lmfdb_iso': '4400.s', 'trace_hash': 1709546828384940214}
• 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': '0.58644601670391309207706959529', 'prec': 103}, 'conductor': 4400, 'gens': [[18, 40, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.22035584825563752770771466299', 'prec': 103}], 'lmfdb_label': '4400.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.2610916432387235563842557777', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9859581362368181864219981329072711037', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [-21, 12, 18]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4400.s2'}
• ec_torsion_growth •

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

  
  
  • id: 228987
    {'degree': 3, 'field': [-8, 2, 0, 1], 'lmfdb_label': '4400.s2', 'torsion': [2]}
  • id: 228988
    {'degree': 4, 'field': [5, 0, -5, 0, 1], 'lmfdb_label': '4400.s2', 'torsion': [5]}
  • id: 228989
    {'degree': 6, 'field': [16, -32, 118, 16, -7, -2, 1], 'lmfdb_label': '4400.s2', 'torsion': [2, 2]}
  • id: 228990
    {'degree': 8, 'field': [-1200, 0, -700, 0, -120, 0, 0, 0, 1], 'lmfdb_label': '4400.s2', 'torsion': [3]}
  • id: 228991
    {'degree': 10, 'field': [968, 0, 0, 0, 0, -44, 0, 0, 0, 0, 1], 'lmfdb_label': '4400.s2', 'torsion': [5]}
  • id: 228992
    {'degree': 12, 'field': [-44000, 0, -54000, 0, 3200, 0, -1000, 0, 370, 0, -35, 0, 1], 'lmfdb_label': '4400.s2', 'torsion': [4]}
  • id: 228993
    {'degree': 12, 'field': [-419, -1550, 689, 762, 816, 226, 13, -14, -6, -10, -1, -2, 1], 'lmfdb_label': '4400.s2', 'torsion': [10]}
  • id: 228994
    {'degree': 20, 'field': [1, -72, 787, -1814, -6419, 20748, 17949, -65992, -15516, 84688, -2270, -48836, 6764, 13960, -2696, -2044, 455, 146, -35, -4, 1], 'lmfdb_label': '4400.s2', 'torsion': [25]}
• 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: 83253
    {'conductor': 4400, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '4400.s2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 83254
    {'conductor': 4400, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '4400.s2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 83255
    {'conductor': 4400, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4400.s2', '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: 1692567
    {'adelic_gens': [[1670, 1209, 787, 2098], [1101, 50, 1125, 1251], [2031, 10, 45, 2021], [1, 50, 0, 1], [38, 41, 1841, 1639], [2151, 50, 2150, 51], [1, 0, 50, 1], [1649, 2150, 0, 2199]], 'adelic_image': '2200.1200.37.?', 'conductor': 4400, 'lmfdb_label': '4400.s2', 'prime': 0}
  • id: 21813
    {'conductor': 4400, 'elladic_image': '25.60.0.2', 'lmfdb_label': '4400.s2', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 156628
    {'lmfdb_iso': '4400.s', 'p': 7, 'prec': 20, 'unit': 112467074366075, 'val': 2}
  • id: 156632
    {'lmfdb_iso': '4400.s', 'p': 13, 'prec': 20, 'unit': 648338636588359739309, 'val': 1}
  • id: 156634
    {'lmfdb_iso': '4400.s', 'p': 17, 'prec': 20, 'unit': 144622051346355242621933, 'val': 1}
  • id: 156635
    {'lmfdb_iso': '4400.s', 'p': 19, 'prec': 20, 'unit': 11493182477335368146878, 'val': 2}
  • id: 156638
    {'lmfdb_iso': '4400.s', 'p': 23, 'prec': 20, 'unit': 32980108062104720826972388, 'val': 1}
  • id: 156631
    {'lmfdb_iso': '4400.s', 'p': 29, 'prec': 20, 'unit': 5262516581023800922437463154, 'val': 1}
  • id: 156642
    {'lmfdb_iso': '4400.s', 'p': 31, 'prec': 20, 'unit': 11595633332483620771474013813, 'val': 1}
  • id: 156627
    {'lmfdb_iso': '4400.s', 'p': 37, 'prec': 20, 'unit': 9183031910034965789689180782, 'val': 2}
  • id: 156629
    {'lmfdb_iso': '4400.s', 'p': 41, 'prec': 20, 'unit': 310787716975590780007695782709, 'val': 1}
  • id: 156630
    {'lmfdb_iso': '4400.s', 'p': 43, 'prec': 20, 'unit': 9470609361785105508228437088522, 'val': 1}
  • id: 156633
    {'lmfdb_iso': '4400.s', 'p': 47, 'prec': 20, 'unit': 56253085644223435101101738685955, 'val': 1}
  • id: 156636
    {'lmfdb_iso': '4400.s', 'p': 53, 'prec': 20, 'unit': 85932644040668055809079027855370, 'val': 1}
  • id: 156641
    {'lmfdb_iso': '4400.s', 'p': 61, 'prec': 20, 'unit': 7517552709091674081438068839551687, 'val': 1}
  • id: 156626
    {'lmfdb_iso': '4400.s', 'p': 67, 'prec': 20, 'unit': 48956587919616180846527586774406899, 'val': 1}
  • id: 156640
    {'lmfdb_iso': '4400.s', 'p': 71, 'prec': 20, 'unit': 44966640067051871553450200241492496, 'val': 1}
  • id: 156637
    {'lmfdb_iso': '4400.s', 'p': 73, 'prec': 20, 'unit': 197271478842414782965887463074748070, 'val': 1}
  • id: 156625
    {'lmfdb_iso': '4400.s', 'p': 83, 'prec': 20, 'unit': 2324875810326858186877426475046945632, 'val': 1}
  • id: 156639
    {'lmfdb_iso': '4400.s', 'p': 89, 'prec': 20, 'unit': 2735627230436752127067139026439557272, 'val': 1}
  • id: 156624
    {'lmfdb_iso': '4400.s', 'p': 97, 'prec': 20, 'unit': 2875958566641302780218492913404886287, 'val': 1}