Elliptic curve data - 630.f8

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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': '630f', 'Clabel': '630f8', 'Cnumber': 8, 'abc_quality': 1.0876511700840974, 'absD': 9889554199218750, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 840, 'ainvs': [1, -1, 0, 6561, 4778595], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 630, 'degree': 4608, 'elladic_images': ['4.6.0.1', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7483321573699796045235652192', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [42841933504271, 13565917968750], 'lmfdb_iso': '630.f', 'lmfdb_label': '630.f8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 729, -176985], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.c.1', '6.24.0-6.a.1.4', '12.48.0-12.g.1.12', '24.96.0-24.bu.2.26', '40.12.0-4.c.1.5', '56.12.0.v.1', '84.96.0.?', '120.192.1.?', '168.192.1.?', '280.24.0.?', '840.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 63], [3, 8, 2], [5, 6, 126], [7, 8, 90]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1990260130359247588259426007', 'prec': 100}, 'szpiro_ratio': 6.870163054377091, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
• 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, 1, 0, 1, -1, 0, -1, 0, 0, 2, -1, 0, 1, 6, 0, -4, 1], 'aplist': [-1, 0, 1, 1, 0, 2, 6, -4, 0, 6, -4, 2, -6, 8, 12, -6, 12, 2, 8, 0, 14, -16, -12, -6, 14], 'class_deg': 12, 'class_size': 8, 'conductor': 630, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '630.f', 'trace_hash': 1292300591239374218}
• 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': '0.030298280576111317533067896810', 'prec': 107}, 'conductor': 630, 'gens': [], 'heights': [], 'lmfdb_label': '630.f8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.31638367698298068638848057229', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2655347079319227455539222891564711452', 'prec': 130}, 'tamagawa_product': 144, 'torsion_generators': [[351, 6912, 1]], 'xcoord_integral_points': [1, 351]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 2], '3': 'a', '5': [1, 0], '7': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '630.f8'}
• ec_torsion_growth •

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

  
  
  • id: 29142
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [12]}
  • id: 29141
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [2, 6]}
  • id: 29143
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [12]}
  • id: 29144
    {'degree': 4, 'field': [25, 0, 4, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [2, 12]}
  • id: 29145
    {'degree': 6, 'field': [48, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [3, 6]}
  • id: 29147
    {'degree': 8, 'field': [-149, 612, -578, -80, 71, -40, 18, -4, 1], 'lmfdb_label': '630.f8', 'torsion': [24]}
  • id: 29148
    {'degree': 8, 'field': [576, 0, 1284, 0, 241, 0, 34, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [24]}
  • id: 29146
    {'degree': 8, 'field': [1500, -1680, 808, -224, 136, -56, 20, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [2, 12]}
  • id: 29149
    {'degree': 9, 'field': [-40620, -75240, -47520, -7554, 3510, 1188, -85, -57, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [18]}
  • id: 29151
    {'degree': 12, 'field': [25, 30, 111, -290, 180, -90, 129, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '630.f8', 'torsion': [3, 12]}
  • id: 29152
    {'degree': 12, 'field': [26244, 0, 0, 0, 0, 0, 1776, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [3, 12]}
  • id: 29150
    {'degree': 12, 'field': [4231249, 12342, 30891, -82370, 30960, 12222, -3975, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '630.f8', 'torsion': [6, 6]}
  • id: 29155
    {'degree': 16, 'field': [9081, -7704, 73392, -78456, -76316, 94776, 32928, -39664, -6187, 5624, 3548, -2008, -90, 168, -4, -8, 1], 'lmfdb_label': '630.f8', 'torsion': [2, 24]}
  • id: 29154
    {'degree': 16, 'field': [14400, 0, -32160, 0, 70996, 0, -11868, 0, -2871, 0, 256, 0, 114, 0, 12, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [2, 24]}
  • id: 29153
    {'degree': 16, 'field': [15625, 70000, 156800, -212240, 125066, -33208, 37632, -25312, 6831, -1736, 1568, -448, 102, -56, 0, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [4, 12]}
  • id: 29157
    {'degree': 18, 'field': [-609638400, 0, 228614400, 0, -330402240, 0, 151068996, 0, -28318896, 0, 3146040, 0, -214530, 0, 8460, 0, -156, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [36]}
  • id: 29158
    {'degree': 18, 'field': [10803852900, 27762215400, 29060331120, 14723624988, 2591996436, -1021649760, -719030538, -150469164, 24271326, 23330118, 4000104, -927450, -326309, 15264, 10557, -86, -162, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [36]}
  • id: 29156
    {'degree': 18, 'field': [15257090016, 0, 24208550352, 0, 4216348080, 0, -299603052, 0, -1841616, 0, 3891384, 0, -277102, 0, 10080, 0, -168, 0, 1], 'lmfdb_label': '630.f8', 'torsion': [2, 18]}
• 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: 7612
    {'conductor': 630, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '630.f8', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7613
    {'conductor': 630, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '630.f8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7614
    {'conductor': 630, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '630.f8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 7615
    {'conductor': 630, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '630.f8', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1668744
    {'adelic_gens': [[246, 409, 35, 176], [1, 12, 12, 145], [699, 556, 832, 387], [337, 24, 684, 289], [15, 106, 374, 11], [631, 24, 642, 289], [817, 24, 816, 25], [496, 21, 195, 466], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '840.384.5.?', 'conductor': 630, 'lmfdb_label': '630.f8', 'prime': 0}
  • id: 2845
    {'conductor': 630, 'elladic_image': '4.6.0.1', 'lmfdb_label': '630.f8', 'modell_image': '2B', 'prime': 2}
  • id: 2846
    {'conductor': 630, 'elladic_image': '3.8.0.1', 'lmfdb_label': '630.f8', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 630.f does not appear in ec_padic