Elliptic curve data - 187200.r3

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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': '187200ks', 'Clabel': '187200ks2', 'Cnumber': 2, 'abc_quality': 1.1039479900506757, 'absD': 7628281189761024000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -18713100, -30873130000], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 187200, 'degree': 15728640, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0152499334285913236886780008', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [242702053576633, 2554695936], 'lmfdb_iso': '187200.r', 'lmfdb_label': '187200.r3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -1299, 17325], 'min_quad_twist_disc': -120, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0.a.1', '40.12.0-2.a.1.1', '52.12.0.b.1', '120.24.0.?', '156.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.524853256124123233339204685', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 8, 20800], [5, 14, 7488], [13, 14, 14400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.62150406203756832656482753354', 'prec': 103}, 'szpiro_ratio': 5.094575641102318, '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, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 1, 0, 0, 0, 2, 0, 8, 0], 'aplist': [0, 0, 0, -4, -4, 1, 2, 8, 0, 6, -4, -2, 10, 4, 8, 10, 4, 2, -16, 8, -2, 8, -12, -14, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 187200, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '187200.r', 'trace_hash': 477664974368575355}
• 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': '0.0024042918523810092321551702345', 'prec': 110}, 'conductor': 187200, 'gens': [[369800, 224864300, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '10.524853256124123233339204685', 'prec': 100}], 'lmfdb_label': '187200.r3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.072633881089601576096373775511', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.1156875191266042247317437125682899545', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-2300, 0, 1], [4990, 0, 1]], 'xcoord_integral_points': [-2690, -2300, 4990, 369800]}
• lmfdb_label 187200.r3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8253345
    {'degree': 4, 'field': [10, -40, 41, -2, 1], 'lmfdb_label': '187200.r3', 'torsion': [2, 4]}
  • id: 8253346
    {'degree': 4, 'field': [25, 0, -20, 0, 1], 'lmfdb_label': '187200.r3', 'torsion': [2, 4]}
  • id: 8253347
    {'degree': 4, 'field': [1119, -54, 55, -2, 1], 'lmfdb_label': '187200.r3', 'torsion': [2, 4]}
  • id: 8253348
    {'degree': 8, 'field': [-7500, 0, -5250, 0, -900, 0, 10, 0, 1], 'lmfdb_label': '187200.r3', 'torsion': [2, 6]}
  • id: 8253351
    {'degree': 16, 'field': [36, 0, -1224, 0, -636, 0, -1968, 0, 3373, 0, -1564, 0, 306, 0, -28, 0, 1], 'lmfdb_label': '187200.r3', 'torsion': [2, 8]}
  • id: 8253349
    {'degree': 16, 'field': [2193361, -1321052, -679412, -307880, 714995, -24728, -19536, -77840, 22664, -5020, 2646, 164, 95, -40, 22, -4, 1], 'lmfdb_label': '187200.r3', 'torsion': [4, 4]}
  • id: 8253350
    {'degree': 16, 'field': [7974976, 0, 2238144, 0, 7647988, 0, -755364, 0, -58287, 0, 1992, 0, 142, 0, 12, 0, 1], 'lmfdb_label': '187200.r3', 'torsion': [2, 8]}
  • id: 8253352
    {'degree': 16, 'field': [67916836, -116932920, 215064252, -141827400, 113810602, -44201220, 21548148, -5810400, 2049243, -391260, 131988, -11880, 5962, -120, 132, 0, 1], 'lmfdb_label': '187200.r3', '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: 4632828
    {'conductor': 187200, 'conductor_valuation': 6, 'discriminant_valuation': 26, 'j_denominator_valuation': 8, 'kodaira_symbol': -20, 'lmfdb_label': '187200.r3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4632829
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 16, 'j_denominator_valuation': 10, 'kodaira_symbol': -14, 'lmfdb_label': '187200.r3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4632830
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '187200.r3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4632831
    {'conductor': 187200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '187200.r3', '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: 2866970
    {'adelic_gens': [[1, 0, 4, 1], [1479, 620, 1240, 1549], [1301, 1250, 0, 1], [623, 0, 0, 1559], [1, 4, 0, 1], [189, 310, 290, 469], [159, 620, 160, 619], [779, 0, 0, 1559], [1557, 4, 1556, 5]], 'adelic_image': '1560.48.0.?', 'conductor': 187200, 'lmfdb_label': '187200.r3', 'prime': 0}
  • id: 699624
    {'conductor': 187200, 'elladic_image': '2.6.0.1', 'lmfdb_label': '187200.r3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 187200.r does not appear in ec_padic