Elliptic curve data - 203280.hc2

Formats: - HTML - YAML - JSON - 2024-10-31T23:59:32.412129

• 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': '203280et', 'Clabel': '203280et4', 'Cnumber': 4, 'abc_quality': 0.9670732682705956, 'absD': 340316159475600000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1848, 'ainvs': [0, 1, 0, -15531600, -23548297500], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 203280, 'degree': 11796480, 'elladic_images': ['8.24.0.17'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8684612130575473408064496081', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 184, 'isogeny_degrees': [1, 2, 4], 'jinv': [228410605013945764, 187597265625], 'lmfdb_iso': '203280.hc', 'lmfdb_label': '203280.hc2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -128360, -17645508], 'min_quad_twist_disc': 44, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0-4.b.1.1', '24.48.0-24.m.1.2', '44.24.0-4.b.1.3', '56.48.0-56.h.2.25', '88.48.0.?', '168.96.0.?', '264.96.0.?', '616.96.0.?', '1848.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.4693963682813791189404018121', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 121], [3, 4, 67760], [5, 6, 40656], [7, 8, 29040], [11, 72, 1680]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0918909261917409775944510512', 'prec': 100}, 'szpiro_ratio': 5.0144871326872, '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, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, -2, 0, 4, 0], 'aplist': [0, 1, 1, 1, 0, 2, -2, 4, 0, 2, 8, -10, 6, -4, 0, -2, 12, -14, -12, 0, 6, -16, -4, -14, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 203280, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '203280.hc', 'trace_hash': 1896355719971684579}
• 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': '0.0032246772021031451575899200296', 'prec': 110}, 'conductor': 203280, 'gens': [[-2310, 2940, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.4693963682813791189404018121', 'prec': 100}], 'lmfdb_label': '203280.hc2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.076053099077370649968856773556', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.019535786124991234174199626704928500', 'prec': 130}, 'tamagawa_product': 1024, 'torsion_generators': [[-2226, 0, 1], [4550, 0, 1]], 'xcoord_integral_points': [-2325, -2310, -2226, 4550, 5760, 43050]}
• lmfdb_label 203280.hc2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8902778
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '203280.hc2', 'torsion': [2, 4]}
  • id: 8902780
    {'degree': 4, 'field': [9, 0, -50, 0, 1], 'lmfdb_label': '203280.hc2', 'torsion': [2, 4]}
  • id: 8902779
    {'degree': 4, 'field': [625, 0, 6, 0, 1], 'lmfdb_label': '203280.hc2', 'torsion': [2, 4]}
  • id: 8902785
    {'degree': 8, 'field': [-43923, 0, -23848, 0, -726, 0, 0, 0, 1], 'lmfdb_label': '203280.hc2', 'torsion': [2, 6]}
  • id: 8902782
    {'degree': 8, 'field': [9, -30, 67, -98, 98, -2, -7, -2, 1], 'lmfdb_label': '203280.hc2', 'torsion': [2, 8]}
  • id: 8902783
    {'degree': 8, 'field': [564, -276, 322, -94, 53, -10, 8, -4, 1], 'lmfdb_label': '203280.hc2', 'torsion': [2, 8]}
  • id: 8902781
    {'degree': 8, 'field': [2825, 1460, -1308, -316, 189, -40, 18, -4, 1], 'lmfdb_label': '203280.hc2', 'torsion': [4, 4]}
  • id: 8902784
    {'degree': 8, 'field': [245025, 0, -86636, 0, -506, 0, -44, 0, 1], 'lmfdb_label': '203280.hc2', 'torsion': [2, 8]}
  • id: 8902787
    {'degree': 16, 'field': [618765625, 0, 245017900, 0, 46819054, 0, 2818080, 0, 28143, 0, 2040, 0, 802, 0, -20, 0, 1], 'lmfdb_label': '203280.hc2', 'torsion': [4, 8]}
  • id: 8902788
    {'degree': 16, 'field': [1299602925, -4325218200, 5058585600, -1522138776, 901865034, -175314376, 68915132, -8731888, 1864115, 225368, -57508, 6304, -626, -224, 52, -8, 1], 'lmfdb_label': '203280.hc2', 'torsion': [2, 12]}
  • id: 8902786
    {'degree': 16, 'field': [295032562561, 0, -41274325972, 0, 4710651242, 0, -196583376, 0, 6634067, 0, 238128, 0, -22, 0, 44, 0, 1], 'lmfdb_label': '203280.hc2', '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: 5033251
    {'conductor': 203280, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '203280.hc2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5033252
    {'conductor': 203280, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '203280.hc2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5033253
    {'conductor': 203280, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '203280.hc2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 5033254
    {'conductor': 203280, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '203280.hc2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5033255
    {'conductor': 203280, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '203280.hc2', 'prime': 11, '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: 2965671
    {'adelic_gens': [[617, 8, 620, 33], [1, 0, 8, 1], [5, 4, 1844, 1845], [1, 8, 0, 1], [7, 6, 1578, 1843], [1841, 8, 1840, 9], [833, 1846, 1026, 5], [3, 470, 454, 1827], [1841, 460, 18, 1391]], 'adelic_image': '1848.192.1.?', 'conductor': 203280, 'lmfdb_label': '203280.hc2', 'prime': 0}
  • id: 752438
    {'conductor': 203280, 'elladic_image': '8.24.0.17', 'lmfdb_label': '203280.hc2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 203280.hc does not appear in ec_padic