Elliptic curve data - 129600.gp1

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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': '129600fy', 'Clabel': '129600fy4', 'Cnumber': 4, 'abc_quality': 1.1259568215438134, 'absD': 278628139008000000, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 2520, 'ainvs': [0, 0, 0, -15511500, 23514138000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 129600, 'degree': 3483648, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6631139502686631789546907180', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 21, 'intrinsic_torsion': 1, 'iso_nlabel': 171, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-189613868625, 128], 'lmfdb_iso': '129600.gp', 'lmfdb_label': '129600.gp1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -1077, 13877], 'min_quad_twist_disc': 120, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '21.64.1.a.4', '24.8.0.a.1', '30.8.0-3.a.1.2', '56.16.0.a.1', '63.192.5.e.1', '70.16.0-7.a.1.1', '120.16.0.?', '168.128.5.?', '210.128.1.?', '280.32.0.?', '504.384.21.?', '630.384.5.?', '840.256.5.?', '2520.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2025], [3, 2, 1600], [5, 14, 5184]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27993806545641466386678236772', 'prec': 107}, 'szpiro_ratio': 5.205895155657575, '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, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, 2, 0, 0, 0, 3, 0, -1, 0], 'aplist': [0, 0, 0, 2, -3, 2, 3, -1, -6, -6, 4, -4, 9, 1, -6, 12, 3, -8, -5, 12, -11, 4, -12, 6, -5], 'class_deg': 21, 'class_size': 4, 'conductor': 129600, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '129600.gp', 'trace_hash': 187248186666553405}
• 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': '0.0048623768320049062614068470967', 'prec': 110}, 'conductor': 129600, 'gens': [], 'heights': [], 'lmfdb_label': '129600.gp1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.25566572931651018448842495020', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0453258345320814759073996016151184149', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [2, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '129600.gp1'}
• ec_torsion_growth •

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

  
  
  • id: 5893114
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [3]}
  • id: 5893115
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [2]}
  • id: 5893118
    {'degree': 6, 'field': [-167286, -10584, 15141, -56, -252, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [7]}
  • id: 5893119
    {'degree': 6, 'field': [-80, -120, 9, -40, 6, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [6]}
  • id: 5893116
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [2, 2]}
  • id: 5893117
    {'degree': 6, 'field': [250, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [3]}
  • id: 5893123
    {'degree': 12, 'field': [-40116, 564984, -1124226, 47040, 804801, 6468, -146264, -1764, 9627, -28, -192, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [21]}
  • id: 5893122
    {'degree': 12, 'field': [784, 0, 1656, 0, 1185, 0, 292, 0, 54, 0, 12, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [2, 6]}
  • id: 5893120
    {'degree': 12, 'field': [6074, 2112, -14577, -15662, 2793, 5904, -555, -1074, 237, 40, -3, -6, 1], 'lmfdb_label': '129600.gp1', 'torsion': [4]}
  • id: 5893121
    {'degree': 12, 'field': [63001, -1506, -3729, 9950, -3660, -1626, 641, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '129600.gp1', 'torsion': [3, 3]}
  • id: 5893126
    {'degree': 18, 'field': [-121692242384, 156592896192, -35541263610, -9194960096, 7843183563, -1598300214, 378906499, -152074008, 18707220, -2933732, 1745424, -266244, 36296, -15084, 414, 712, -87, -6, 1], 'lmfdb_label': '129600.gp1', 'torsion': [14]}
  • id: 5893124
    {'degree': 18, 'field': [-187500000, 0, 337500000, 0, -219375000, 0, 68062500, 0, -11700000, 0, 1215000, 0, -83250, 0, 3600, 0, -90, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [9]}
  • id: 5893125
    {'degree': 18, 'field': [177875, 277500, -125100, -279750, 138420, 210780, -65841, -98484, 14220, 30908, 1584, -6084, -1275, 672, 252, -30, -24, 0, 1], 'lmfdb_label': '129600.gp1', 'torsion': [6]}
• 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: 3196308
    {'conductor': 129600, 'conductor_valuation': 6, 'discriminant_valuation': 25, 'j_denominator_valuation': 7, 'kodaira_symbol': -19, 'lmfdb_label': '129600.gp1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3196309
    {'conductor': 129600, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '129600.gp1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3196310
    {'conductor': 129600, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '129600.gp1', 'prime': 5, '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: 2508491
    {'adelic_gens': [[1, 0, 1470, 1], [281, 1400, 1120, 1401], [1, 930, 1050, 1261], [503, 0, 0, 2519], [419, 1470, 315, 1469], [209, 1470, 1785, 2309], [1, 720, 0, 1], [1, 1680, 0, 1], [1471, 1290, 420, 2311], [526, 825, 2205, 1681], [505, 2016, 504, 505], [1, 0, 1680, 1], [1081, 1410, 0, 1], [1, 0, 2016, 1], [841, 1680, 840, 1681], [39, 1070, 560, 2319], [1, 0, 420, 1]], 'adelic_image': '2520.768.21.?', 'conductor': 129600, 'lmfdb_label': '129600.gp1', 'prime': 0}
  • id: 504971
    {'conductor': 129600, 'elladic_image': '8.2.0.1', 'lmfdb_label': '129600.gp1', 'modell_image': '2G', 'prime': 2}
  • id: 504972
    {'conductor': 129600, 'elladic_image': '3.4.0.1', 'lmfdb_label': '129600.gp1', 'modell_image': '3B', 'prime': 3}
  • id: 504973
    {'conductor': 129600, 'elladic_image': '7.8.0.1', 'lmfdb_label': '129600.gp1', 'modell_image': '7B', 'prime': 7}
• lmfdb_iso 129600.gp does not appear in ec_padic