Elliptic curve data - 302016.r4

Formats: - HTML - YAML - JSON - 2024-05-24T05:33:44.300558

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '302016r', 'Clabel': '302016r4', 'Cnumber': 4, 'abc_quality': 0.9950166304018127, 'absD': 8735437067892660043776, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3432, 'ainvs': [0, -1, 0, 1262111, 4463106529], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 302016, 'degree': 20643840, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8900006910838763486469551615', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [1915049403068, 75239967231], 'lmfdb_iso': '302016.r', 'lmfdb_label': '302016.r4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 2608, -418320], 'min_quad_twist_disc': -88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '78.6.0.?', '88.12.0.?', '104.12.0.?', '156.12.0.?', '264.24.0.?', '312.24.0.?', '1144.24.0.?', '3432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.708709625343027492330516856', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.76685681393809733072634054391', 'prec': 103}, 'szpiro_ratio': 4.593475598884176, '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, 0, -1, 0, -2, 0, -4, 0, 1, 0, 0, 0, 1, 0, 2, 0, 6, 0, 0, 0], 'aplist': [0, -1, -2, -4, 0, 1, 6, 0, 8, -2, 4, -6, 2, -4, 0, -6, 12, 14, 0, 0, 6, 0, -4, 6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 302016, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '302016.r', 'trace_hash': 1194501954634412437}
• 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': '0.0030887111391168854861911259458', 'prec': 110}, 'conductor': 302016, 'gens': [[233479, 112934240, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '11.708709625343027492330516856', 'prec': 100}], 'lmfdb_label': '302016.r4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.098629923076575190863922107979', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6193165186941532979453048586393762643', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-1393, 0, 1]], 'xcoord_integral_points': [-1393]}
• lmfdb_label 302016.r4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12771167
    {'degree': 2, 'field': [-286, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [4]}
  • id: 12771166
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '302016.r4', 'torsion': [2, 2]}
  • id: 12771168
    {'degree': 2, 'field': [66, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [4]}
  • id: 12771169
    {'degree': 4, 'field': [3202, -152, 153, -2, 1], 'lmfdb_label': '302016.r4', 'torsion': [2, 4]}
  • id: 12771173
    {'degree': 8, 'field': [-702768, 0, 66880, 0, -2904, 0, 0, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [6]}
  • id: 12771171
    {'degree': 8, 'field': [8464, 0, -4208, 0, 188, 0, 4, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [8]}
  • id: 12771170
    {'degree': 8, 'field': [79524, 0, -16038, 0, 1653, 0, -66, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [2, 4]}
  • id: 12771172
    {'degree': 8, 'field': [300001, 18252, 46738, 564, 2775, -12, 82, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [8]}
  • id: 12771178
    {'degree': 16, 'field': [-1835885402, -8369164336, -6320877312, 10928573704, 10290455846, 2969318748, 941623240, 205711460, 40267026, 7412624, 841378, 143652, 15614, 460, 240, -4, 1], 'lmfdb_label': '302016.r4', 'torsion': [12]}
  • id: 12771179
    {'degree': 16, 'field': [22268961, 0, 6882797988, 0, 1098859564, 0, 110510268, 0, 6447606, 0, 265628, 0, 7260, 0, 132, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [12]}
  • id: 12771175
    {'degree': 16, 'field': [71639296, 0, 35616512, 0, 16116032, 0, 858816, 0, 43712, 0, -9168, 0, -172, 0, -4, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [2, 8]}
  • id: 12771174
    {'degree': 16, 'field': [4234625476, 0, 1590034040, 0, 422066200, 0, 61508300, 0, 5255941, 0, 271040, 0, 8350, 0, 140, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [4, 4]}
  • id: 12771176
    {'degree': 16, 'field': [52622066025, 0, 18599287302, 0, 2990072517, 0, 279339306, 0, 16315348, 0, 604102, 0, 13797, 0, 178, 0, 1], 'lmfdb_label': '302016.r4', 'torsion': [2, 8]}
  • id: 12771177
    {'degree': 16, 'field': [2599633943248, 122590573696, -119487676992, -6507885120, 4009634856, -908421504, 306338320, -4777136, 3361497, -1413048, 252012, 15192, -1258, -616, 108, -8, 1], 'lmfdb_label': '302016.r4', 'torsion': [2, 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: 7478852
    {'conductor': 302016, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '302016.r4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 7478853
    {'conductor': 302016, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '302016.r4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7478854
    {'conductor': 302016, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '302016.r4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7478855
    {'conductor': 302016, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '302016.r4', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 3562994
    {'adelic_gens': [[1517, 1518, 1430, 2837], [7, 6, 3426, 3427], [3425, 8, 3424, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1915, 352, 2090, 45], [892, 2497, 1463, 2190], [2608, 627, 1045, 2498], [2495, 0, 0, 3431]], 'adelic_image': '3432.48.0.?', 'conductor': 302016, 'lmfdb_label': '302016.r4', 'prime': 0}
  • id: 1064248
    {'conductor': 302016, 'elladic_image': '4.6.0.1', 'lmfdb_label': '302016.r4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 302016.r does not appear in ec_padic