Elliptic curve data - 12870.f2

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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': '12870k', 'Clabel': '12870k3', 'Cnumber': 3, 'abc_quality': 0.9996929468325244, 'absD': 906961409640000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 17160, 'ainvs': [1, -1, 0, -3346200, 2356839936], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 12870, 'degree': 245760, 'elladic_images': ['8.24.0.15'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2536934956865123495335809860', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4], 'jinv': [5683972151443376419201, 1244117160000], 'lmfdb_iso': '12870.f', 'lmfdb_label': '12870.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -371800, -87290368], 'min_quad_twist_disc': -3, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.d.1', '12.24.0-4.b.1.1', '24.48.0-8.d.1.1', '88.48.0.?', '264.96.0.?', '520.48.0.?', '1560.96.0.?', '5720.96.0.?', '17160.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0019633547177306487428306774', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 715], [5, 6, 2574], [11, 12, 1170], [13, 14, 990]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7043873513524575038359583675', 'prec': 100}, 'szpiro_ratio': 5.990244300915296, '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, 0, 1, -1, 0, 0, -1, 0, 1, -1, 0, 1, 0, 0, 1, -2, 0, 4, -1], 'aplist': [-1, 0, -1, 0, -1, 1, -2, 4, 0, 2, 8, -10, -10, -4, 8, 10, -12, -2, 4, 0, 10, -8, -4, -18, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 12870, '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': '12870.f', 'trace_hash': 1098709345470323818}
• 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': '0.011027236827575903437771377938', 'prec': 107}, 'conductor': 12870, 'gens': [[1047, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0019633547177306487428306774', 'prec': 100}], 'lmfdb_label': '12870.f2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.39515284454202792761443896004', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1674293579486736302396568171016932925', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-2112, 1056, 1], [1056, -528, 1]], 'xcoord_integral_points': [-2112, 813, 1047, 1056, 1320, 1563]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [2, 0], '17': [3, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [3, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '12870.f2'}
• ec_torsion_growth •

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

  
  
  • id: 662954
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 4]}
  • id: 662956
    {'degree': 4, 'field': [484, 0, -22, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 4]}
  • id: 662955
    {'degree': 4, 'field': [484, 0, 22, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 4]}
  • id: 662960
    {'degree': 8, 'field': [-62208, 0, 15579, 0, -864, 0, 0, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 6]}
  • id: 662957
    {'degree': 8, 'field': [14641, 0, 0, 0, -121, 0, 0, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [4, 4]}
  • id: 662959
    {'degree': 8, 'field': [65536, 0, -8448, 0, 833, 0, -33, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 8]}
  • id: 662958
    {'degree': 8, 'field': [98206, 41332, -36254, -10004, 4623, 452, -146, -4, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 8]}
  • id: 662964
    {'degree': 16, 'field': [627264, 0, -1682211, 0, 1127290, 0, 17403, 0, -20565, 0, -2137, 0, 15, 0, -6, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 12]}
  • id: 662961
    {'degree': 16, 'field': [24010000, 0, 7604800, 0, 1644304, 0, 320512, 0, 31852, 0, -4352, 0, -92, 0, -8, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 8]}
  • id: 662963
    {'degree': 16, 'field': [2826509481, 3907198152, 822649410, 241436712, 1396108492, 66087692, 77481074, 5842584, 5904645, 56980, 254078, -1496, 7316, -44, 132, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [4, 8]}
  • id: 662962
    {'degree': 16, 'field': [4342593057136, 1926061262400, -302213311776, -155926049664, 32500846144, 7392240768, -2107467792, -186318528, 72290628, 1522752, -1523592, 8448, 23404, -264, -216, 0, 1], 'lmfdb_label': '12870.f2', 'torsion': [2, 8]}
• 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: 278955
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '12870.f2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 278956
    {'conductor': 12870, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '12870.f2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 278957
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12870.f2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 278958
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12870.f2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 278959
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12870.f2', 'prime': 13, 'reduction_type': 1, '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: 1749380
    {'adelic_gens': [[5, 4, 17156, 17157], [17153, 8, 17152, 9], [3127, 6, 4674, 17155], [1, 0, 8, 1], [2641, 8, 10564, 33], [10297, 8, 6868, 33], [1, 4294, 0, 12871], [3, 12874, 12866, 17155], [5713, 17154, 6, 5], [1, 8, 0, 1]], 'adelic_image': '17160.192.1.?', 'conductor': 12870, 'lmfdb_label': '12870.f2', 'prime': 0}
  • id: 61141
    {'conductor': 12870, 'elladic_image': '8.24.0.15', 'lmfdb_label': '12870.f2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 564866
    {'lmfdb_iso': '12870.f', 'p': 17, 'prec': 20, 'unit': 6573294134430748688586, 'val': 2}
  • id: 564858
    {'lmfdb_iso': '12870.f', 'p': 19, 'prec': 20, 'unit': 1399383746472624064195896, 'val': 1}
  • id: 564864
    {'lmfdb_iso': '12870.f', 'p': 29, 'prec': 20, 'unit': 4135495404564567626811073624, 'val': 1}
  • id: 564874
    {'lmfdb_iso': '12870.f', 'p': 31, 'prec': 20, 'unit': 17576964629544275569417045995, 'val': 1}
  • id: 564861
    {'lmfdb_iso': '12870.f', 'p': 37, 'prec': 20, 'unit': 347377514902102666491284442890, 'val': 1}
  • id: 564862
    {'lmfdb_iso': '12870.f', 'p': 41, 'prec': 20, 'unit': 3027933554258358088173767024028, 'val': 1}
  • id: 564863
    {'lmfdb_iso': '12870.f', 'p': 43, 'prec': 20, 'unit': 173510958719951688185553332887, 'val': 2}
  • id: 564872
    {'lmfdb_iso': '12870.f', 'p': 47, 'prec': 20, 'unit': 57901989566083943878802424402968, 'val': 1}
  • id: 564868
    {'lmfdb_iso': '12870.f', 'p': 53, 'prec': 20, 'unit': 115354326299742797475991656382229, 'val': 1}
  • id: 564869
    {'lmfdb_iso': '12870.f', 'p': 59, 'prec': 20, 'unit': 372209556778524056678612658697358, 'val': 1}
  • id: 564873
    {'lmfdb_iso': '12870.f', 'p': 61, 'prec': 20, 'unit': 672122816643107457566405095578727, 'val': 1}
  • id: 564860
    {'lmfdb_iso': '12870.f', 'p': 67, 'prec': 20, 'unit': 21786725203340756366122525015605364, 'val': 1}
  • id: 564870
    {'lmfdb_iso': '12870.f', 'p': 73, 'prec': 20, 'unit': 200888393652272180792239881666685919, 'val': 1}
  • id: 564865
    {'lmfdb_iso': '12870.f', 'p': 79, 'prec': 20, 'unit': 22550388137077844039724521757514439, 'val': 1}
  • id: 564867
    {'lmfdb_iso': '12870.f', 'p': 83, 'prec': 20, 'unit': 1078434752023697119098845529239149030, 'val': 1}
  • id: 564871
    {'lmfdb_iso': '12870.f', 'p': 89, 'prec': 20, 'unit': 6549418103478311502083732006100794348, 'val': 1}
  • id: 564859
    {'lmfdb_iso': '12870.f', 'p': 97, 'prec': 20, 'unit': 6581746525295205287565809998806632065, 'val': 1}