Elliptic curve data - 2730.w3

Formats: - HTML - YAML - JSON - 2024-05-15T05:18:27.253923

• 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': '2730v', 'Clabel': '2730v5', 'Cnumber': 5, 'abc_quality': 1.030870999132727, 'absD': 16775330746084419600, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 7280, 'ainvs': [1, 1, 1, -688720, -98092255], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 2730, 'degree': 65536, 'elladic_images': ['8.96.0.58'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3834247019504635589370316971', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 22, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [36128658497509929012481, 16775330746084419600], 'lmfdb_iso': '2730.w', 'lmfdb_label': '2730.w3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -688720, -98092255], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.1', '8.96.0-8.k.1.1', '112.192.1.?', '260.48.0.?', '520.192.1.?', '1040.384.5.?', '7280.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.3834247019504635589370316971', 'prec': 100}, 'szpiro_ratio': 6.564838208515684, '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, 1, -1, 1, 1, -1, -1, 1, 1, 1, 4, -1, 1, -1, -1, 1, 2, 1, -4, 1], 'aplist': [1, -1, 1, -1, 4, 1, 2, -4, 0, -2, 8, 6, -6, 4, 0, 6, -12, -2, 4, 0, 10, 0, 4, 10, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 2730, 'isogeny_matrix': [[1, 16, 2, 4, 8, 8, 16, 4], [16, 1, 8, 4, 2, 8, 4, 16], [2, 8, 1, 2, 4, 4, 8, 2], [4, 4, 2, 1, 2, 2, 4, 4], [8, 2, 4, 2, 1, 4, 2, 8], [8, 8, 4, 2, 4, 1, 8, 8], [16, 4, 8, 4, 2, 8, 1, 16], [4, 16, 2, 4, 8, 8, 16, 1]], 'lmfdb_iso': '2730.w', 'trace_hash': 1550881519414641085}
• 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': '0.0085071405460520283976974579988', 'prec': 110}, 'conductor': 2730, 'gens': [], 'heights': [], 'lmfdb_label': '2730.w3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.17329546552504538348169044511', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7727274484007261357070471216887869249', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-147, 73, 1], [893, -447, 1]], 'xcoord_integral_points': [-147, 893]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 2], '3': [0, 0], '5': [1, 0], '7': [0, 0], '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '2730.w3'}
• ec_torsion_growth •

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

  
  
  • id: 141858
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 4]}
  • id: 141857
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 4]}
  • id: 141859
    {'degree': 2, 'field': [65, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 4]}
  • id: 141863
    {'degree': 4, 'field': [-260, 0, 0, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 8]}
  • id: 141862
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 8]}
  • id: 141860
    {'degree': 4, 'field': [256, 0, 33, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [4, 4]}
  • id: 141861
    {'degree': 4, 'field': [4225, 0, 0, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 8]}
  • id: 141867
    {'degree': 8, 'field': [-256, 1024, -1024, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 6]}
  • id: 141864
    {'degree': 8, 'field': [256, 32, 2, -70, 41, -10, 8, -4, 1], 'lmfdb_label': '2730.w3', 'torsion': [4, 8]}
  • id: 141865
    {'degree': 8, 'field': [4356, 0, -776, 0, 136, 0, 4, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [4, 8]}
  • id: 141866
    {'degree': 8, 'field': [65536, 0, 0, 0, 577, 0, 0, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [4, 8]}
  • id: 141872
    {'degree': 16, 'field': [-303664, -24960, 9836352, -1580800, -2063072, -1297920, 681344, 432640, 159880, -10400, -9936, -4160, -72, 0, 32, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 16]}
  • id: 141868
    {'degree': 16, 'field': [15876, 57456, 103968, -148872, 93928, -19992, 10536, -11876, 7573, -3028, 1064, -484, 178, -76, 32, -8, 1], 'lmfdb_label': '2730.w3', 'torsion': [8, 8]}
  • id: 141874
    {'degree': 16, 'field': [65536, 0, 524288, 0, 1048576, 0, -2559, 0, -6654, 0, 2049, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 12]}
  • id: 141871
    {'degree': 16, 'field': [17872002, 3118824, -1336644, -3155688, 563206, 1197528, -364644, -32440, 12995, -5464, 3548, -1672, 582, -168, 44, -8, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 16]}
  • id: 141875
    {'degree': 16, 'field': [2808152064, 0, -4285882368, 0, 640500480, 0, -55972481, 0, 4451810, 0, -242369, 0, 7393, 0, -130, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 12]}
  • id: 141873
    {'degree': 16, 'field': [4569760000, 0, 562432000, 0, 17305600, 0, 1116350625, 0, 33943650, 0, 282945, 0, 4225, 0, 130, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 12]}
  • id: 141869
    {'degree': 16, 'field': [315101764223236, 0, 12301135282800, 0, 202749474456, 0, -229778640, 0, 33723016, 0, -1146600, 0, 4356, 0, 0, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 16]}
  • id: 141870
    {'degree': 16, 'field': [322380085862916, 0, 12254390694000, 0, 53613008536, 0, 724192560, 0, 46361096, 0, -1146600, 0, -3964, 0, 0, 0, 1], 'lmfdb_label': '2730.w3', 'torsion': [2, 16]}
• 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: 48230
    {'conductor': 2730, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '2730.w3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 48231
    {'conductor': 2730, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '2730.w3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 48232
    {'conductor': 2730, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2730.w3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 48233
    {'conductor': 2730, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '2730.w3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 48234
    {'conductor': 2730, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2730.w3', 'prime': 13, 'reduction_type': 1, '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: 1681840
    {'adelic_gens': [[1049, 8, 6196, 7241], [1, 16, 0, 1], [13, 8, 4410, 7237], [5, 8, 4286, 7149], [1, 0, 16, 1], [9, 8, 7218, 855], [1, 16, 0, 5461], [1, 16, 4, 65], [7265, 16, 7264, 17]], 'adelic_image': '7280.768.13.?', 'conductor': 2730, 'lmfdb_label': '2730.w3', 'prime': 0}
  • id: 13709
    {'conductor': 2730, 'elladic_image': '8.96.0.58', 'lmfdb_label': '2730.w3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 2730.w does not appear in ec_padic