Elliptic curve data - 303450.bc3

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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': '303450bc', 'Clabel': '303450bc5', 'Cnumber': 5, 'abc_quality': 1.0817271650752718, 'absD': 79173093645577037501580646125000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1360, 'ainvs': [1, 1, 0, -2114064050, -429734287366500], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 303450, 'degree': 1132462080, 'elladic_images': ['16.48.0.204'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.8004545975681759899599540967', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-2770540998624539614657, 209924951154647363208], 'lmfdb_iso': '303450.bc', 'lmfdb_label': '303450.bc3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -292604, -699871003], 'min_quad_twist_disc': 85, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.k.1', '16.48.0.e.1', '40.48.0-8.k.1.5', '80.96.0.?', '136.48.0.?', '272.96.1.?', '340.12.0.?', '680.96.0.?', '1360.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 7225], [3, 4, 50575], [5, 14, 12138], [7, 8, 43350], [17, 162, 1050]], 'sha': 16, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5791289693230177625348071211', 'prec': 100}, 'szpiro_ratio': 6.409862668726407, '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, -1, -1, 1, 0, 1, 1, -1, 1, 0, -4, -1, 2, -1, 0, 1, 0, -1, 4, 0], 'aplist': [-1, -1, 0, 1, -4, 2, 0, 4, 8, -6, 0, -2, -10, 4, 0, -6, -4, -6, 12, 8, -6, 0, 12, -6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 303450, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '303450.bc', 'trace_hash': 491839761309427564}
• 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': '0.000067667185838062200211423969509', 'prec': 117}, 'conductor': 303450, 'gens': [], 'heights': [], 'lmfdb_label': '303450.bc3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.0085086882789096973533876106842', 'prec': 110}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0891120997004412612336141675806873215', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[339035, -339035, 2]], 'xcoord_integral_points': []}
• lmfdb_label 303450.bc3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12826762
    {'degree': 2, 'field': [-170, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [4]}
  • id: 12826761
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [2, 2]}
  • id: 12826763
    {'degree': 2, 'field': [85, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [4]}
  • id: 12826766
    {'degree': 4, 'field': [121, 0, -12, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [8]}
  • id: 12826765
    {'degree': 4, 'field': [341, -32, 33, -2, 1], 'lmfdb_label': '303450.bc3', 'torsion': [8]}
  • id: 12826764
    {'degree': 4, 'field': [1849, 0, -84, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [2, 4]}
  • id: 12826771
    {'degree': 8, 'field': [-4099116, -116019, -137096, -36774, -1815, -423, -54, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [6]}
  • id: 12826769
    {'degree': 8, 'field': [3449, 1748, -1308, -844, 333, 104, -30, -4, 1], 'lmfdb_label': '303450.bc3', 'torsion': [2, 8]}
  • id: 12826770
    {'degree': 8, 'field': [65621, 18092, -16284, -3544, 1593, 212, -66, -4, 1], 'lmfdb_label': '303450.bc3', 'torsion': [16]}
  • id: 12826768
    {'degree': 8, 'field': [109319, 62132, -59682, -4816, 2199, 248, -78, -4, 1], 'lmfdb_label': '303450.bc3', 'torsion': [8]}
  • id: 12826767
    {'degree': 8, 'field': [777924, 0, 0, 0, 10094, 0, 0, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [2, 4]}
  • id: 12826776
    {'degree': 16, 'field': [8730281, 9697548, -8242260, -5860580, 2863940, -1617720, 2020368, -1272212, 578133, -131240, 65460, -5100, 3634, -68, 96, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [2, 16]}
  • id: 12826774
    {'degree': 16, 'field': [23059204, 0, 0, 0, 609826560, 0, 0, 0, -1444814, 0, 0, 0, -1680, 0, 0, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [16]}
  • id: 12826773
    {'degree': 16, 'field': [7511386841, -854006888, 987606760, -151065432, -198725576, 284919320, -23781296, -56164976, 8109081, 3741016, -537628, -110824, 15134, 1512, -196, -8, 1], 'lmfdb_label': '303450.bc3', 'torsion': [2, 8]}
  • id: 12826772
    {'degree': 16, 'field': [37822859361, 0, -26415965268, 0, 9224622792, 0, -1104824952, 0, 73141663, 0, -2505272, 0, 47432, 0, -308, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [4, 4]}
  • id: 12826779
    {'degree': 16, 'field': [45193657744, 0, 15188041253, 0, 2445719986, 0, 233680467, 0, 14022675, 0, 535791, 0, 12679, 0, 170, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [12]}
  • id: 12826778
    {'degree': 16, 'field': [11569576382464, 0, -1944069280384, 0, 156526079104, 0, -7477774944, 0, 224362800, 0, -4286328, 0, 50716, 0, -340, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [12]}
  • id: 12826777
    {'degree': 16, 'field': [14686101514834, -690845960016, 1073784447457, 301356910296, 34228182856, 14256337986, 2907659406, 292003272, 51526167, 6778476, 146829, -31248, -1682, -846, -92, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [2, 6]}
  • id: 12826775
    {'degree': 16, 'field': [74591351288561, 56293384229096, 45187928174104, 2840770233392, 2916618817752, -114402406440, 28958582888, -4016400416, -1420860386, 53038776, -1681496, 344624, 233848, -952, -936, 0, 1], 'lmfdb_label': '303450.bc3', 'torsion': [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: 7514470
    {'conductor': 303450, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '303450.bc3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7514471
    {'conductor': 303450, 'conductor_valuation': 1, 'discriminant_valuation': 32, 'j_denominator_valuation': 32, 'kodaira_symbol': 36, 'lmfdb_label': '303450.bc3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7514472
    {'conductor': 303450, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '303450.bc3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7514473
    {'conductor': 303450, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '303450.bc3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7514474
    {'conductor': 303450, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '303450.bc3', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 3571303
    {'adelic_gens': [[15, 2, 1262, 1347], [356, 885, 295, 146], [543, 0, 0, 1359], [1, 16, 0, 1], [1345, 16, 1344, 17], [926, 885, 1065, 146], [1219, 800, 1040, 859], [5, 4, 1356, 1357], [1, 0, 16, 1]], 'adelic_image': '1360.192.1.?', 'conductor': 303450, 'lmfdb_label': '303450.bc3', 'prime': 0}
  • id: 1068194
    {'conductor': 303450, 'elladic_image': '16.48.0.204', 'lmfdb_label': '303450.bc3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 303450.bc does not appear in ec_padic