Elliptic curve data - 277440.es2

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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': '277440es', 'Clabel': '277440es4', 'Cnumber': 4, 'abc_quality': 0.98174487513138, 'absD': 25946782139842560, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 4080, 'ainvs': [0, -1, 0, -92865, -7623135], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 277440, 'degree': 2359296, 'elladic_images': ['8.12.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8554997032428822568010436873', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 122, 'isogeny_degrees': [1, 2, 4], 'jinv': [111980168, 32805], 'lmfdb_iso': '277440.es', 'lmfdb_label': '277440.es2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -80, -168], 'min_quad_twist_disc': 136, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.o.1', '40.24.0.by.1', '48.24.0.j.1', '80.48.0.?', '136.24.0.?', '240.96.3.?', '340.12.0.?', '680.48.0.?', '816.48.0.?', '1360.96.0.?', '4080.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.7660208144692337422261391190', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1445], [3, 4, 92480], [5, 6, 55488], [17, 146, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.42754094448515742009526377346', 'prec': 107}, 'szpiro_ratio': 3.6646454115571316, '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, -1, 0, 1, 0, 4, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0], 'aplist': [0, -1, 1, 4, 0, 2, 0, 0, 4, -2, 8, 6, 6, -12, -12, 10, -8, -10, 12, -8, -10, -16, -12, -6, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 277440, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '277440.es', 'trace_hash': 656533079531288421}
• 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': '0.024453072496306406584586620781', 'prec': 107}, 'conductor': 277440, 'gens': [[-4457, 86064, 7]], 'heights': [{'__RealLiteral__': 0, 'data': '8.7660208144692337422261391190', 'prec': 100}], 'lmfdb_label': '277440.es2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27963335122364301520453710587', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.8050871089849617761383882714852509473', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-249, 0, 1]], 'xcoord_integral_points': [-249]}
• lmfdb_label 277440.es2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11826420
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [2, 2]}
  • id: 11826421
    {'degree': 2, 'field': [34, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [4]}
  • id: 11826422
    {'degree': 2, 'field': [85, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [4]}
  • id: 11826423
    {'degree': 4, 'field': [121, 0, 12, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [2, 4]}
  • id: 11826427
    {'degree': 8, 'field': [-15009315, -5805300, -775270, 105948, 24324, -1168, -318, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [6]}
  • id: 11826424
    {'degree': 8, 'field': [-2724, 7120, -2104, -480, 536, -40, -44, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [2, 4]}
  • id: 11826425
    {'degree': 8, 'field': [2690, -2640, 2828, -1144, 662, -128, 48, -4, 1], 'lmfdb_label': '277440.es2', 'torsion': [8]}
  • id: 11826426
    {'degree': 8, 'field': [93601, 55560, 25424, 5040, 566, -120, -16, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [2, 8]}
  • id: 11826429
    {'degree': 16, 'field': [882009, -772092, 743184, -1082676, 775552, -506376, 295440, -93884, 18025, -1456, 596, -388, 106, -28, 20, -8, 1], 'lmfdb_label': '277440.es2', 'torsion': [2, 8]}
  • id: 11826428
    {'degree': 16, 'field': [1466521, -1550080, 819200, 370000, -381254, 169960, 80000, -7520, 30431, 10360, 800, 1120, 166, -40, 0, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [4, 4]}
  • id: 11826431
    {'degree': 16, 'field': [9262262, -11310904, 1301428, 2901104, 1800048, -273328, 2015156, -629912, 538944, -124652, 61444, -9568, 3390, -316, 92, -4, 1], 'lmfdb_label': '277440.es2', 'torsion': [12]}
  • id: 11826430
    {'degree': 16, 'field': [63351883204, 0, -41067239888, 0, 8559676480, 0, 92811144, 0, -5816100, 0, -191904, 0, -692, 0, -20, 0, 1], 'lmfdb_label': '277440.es2', 'torsion': [2, 6]}
  • id: 11826432
    {'degree': 16, 'field': [128659493600, -122082660800, 73716941440, -26420467520, 8778919536, -1885912688, 512182556, -85785460, 21821625, -2868988, 633004, -62468, 12750, -980, 176, -8, 1], 'lmfdb_label': '277440.es2', 'torsion': [12]}
• 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: 6873286
    {'conductor': 277440, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '277440.es2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6873287
    {'conductor': 277440, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '277440.es2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6873288
    {'conductor': 277440, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '277440.es2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6873289
    {'conductor': 277440, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '277440.es2', 'prime': 17, '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: 3415531
    {'adelic_gens': [[4065, 16, 4064, 17], [3758, 1683, 1581, 3860], [1, 16, 0, 1], [1, 8, 8, 65], [3773, 2210, 1088, 2107], [3839, 0, 0, 4079], [15, 166, 3794, 915], [2566, 1377, 867, 220], [1, 0, 16, 1], [1361, 2176, 1768, 1089]], 'adelic_image': '4080.192.3.?', 'conductor': 277440, 'lmfdb_label': '277440.es2', 'prime': 0}
  • id: 988609
    {'conductor': 277440, 'elladic_image': '8.12.0.10', 'lmfdb_label': '277440.es2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 277440.es does not appear in ec_padic