Elliptic curve data - 244608.m1

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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': '244608m', 'Clabel': '244608m2', 'Cnumber': 2, 'abc_quality': 0.9034676039421148, 'absD': 38464118784, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 728, 'ainvs': [0, -1, 0, -6169, 188329], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 244608, 'degree': 327680, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.93217859736220438582066334635', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2], 'jinv': [9241752992, 13689], 'lmfdb_iso': '244608.m', 'lmfdb_label': '244608.m1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -6169, 188329], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '56.6.0.a.1', '104.6.0.?', '364.6.0.?', '728.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 19, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.0917014151535816010544739859', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 7], [3, 4, 81536], [7, 20, 4992], [13, 14, 18816]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.30520838550823135899100963776', 'prec': 107}, 'szpiro_ratio': 3.046214680603844, '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, 0, 0, 1, 0, -4, 0, 1, 0, 2, 0, 4, 0, -6, 0], 'aplist': [0, -1, -2, 0, -4, 1, 4, -6, 6, -10, -4, -4, -2, 4, 8, 6, -6, -6, 12, -16, -6, -14, -6, -14, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 244608, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '244608.m', 'trace_hash': 42918436905824724}
• 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': '0.15499580999409841808954266829', 'prec': 103}, 'conductor': 244608, 'gens': [[49, 36, 1], [40, 63, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.99876668099333543128074845877', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.1967881102812761242884400199', 'prec': 100}], 'lmfdb_label': '244608.m1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.1508038881023866778738784273', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.050673865644956037972324346767605228', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[47, 0, 1]], 'xcoord_integral_points': [-79, -5, 21, 33, 40, 47, 49, 72, 229, 769]}
• lmfdb_label 244608.m1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10549103
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '244608.m1', 'torsion': [2, 2]}
  • id: 10549104
    {'degree': 4, 'field': [1134, 0, -70, 0, 1], 'lmfdb_label': '244608.m1', 'torsion': [4]}
  • id: 10549107
    {'degree': 8, 'field': [-6732012, 0, 113680, 0, -8988, 0, 0, 0, 1], 'lmfdb_label': '244608.m1', 'torsion': [6]}
  • id: 10549106
    {'degree': 8, 'field': [-25000, -41440, -7696, 10080, 3204, -280, -124, 0, 1], 'lmfdb_label': '244608.m1', 'torsion': [2, 4]}
  • id: 10549105
    {'degree': 8, 'field': [105625, 0, 13100, 0, 626, 0, 20, 0, 1], 'lmfdb_label': '244608.m1', 'torsion': [2, 4]}
  • id: 10549108
    {'degree': 16, 'field': [13351716, 0, -38123568, 0, 15107512, 0, -2416792, 0, 254396, 0, -25336, 0, 1928, 0, -76, 0, 1], 'lmfdb_label': '244608.m1', 'torsion': [8]}
  • id: 10549109
    {'degree': 16, 'field': [4301385259158, -6848592477048, 3655106840448, -864816423408, 62461203732, 16503495120, -4570912584, 440570592, -16088388, -530712, -137564, 1512, -12372, -1512, -84, 0, 1], 'lmfdb_label': '244608.m1', '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: 6064735
    {'conductor': 244608, 'conductor_valuation': 7, 'discriminant_valuation': 13, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '244608.m1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6064736
    {'conductor': 244608, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '244608.m1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6064737
    {'conductor': 244608, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '244608.m1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6064738
    {'conductor': 244608, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '244608.m1', '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: 3218483
    {'adelic_gens': [[1, 2, 2, 5], [725, 4, 724, 5], [1, 4, 0, 1], [2, 1, 363, 0], [92, 641, 457, 282], [561, 4, 394, 9], [1, 0, 4, 1], [3, 4, 8, 11], [628, 1, 207, 0]], 'adelic_image': '728.12.0.?', 'conductor': 244608, 'lmfdb_label': '244608.m1', 'prime': 0}
  • id: 885181
    {'conductor': 244608, 'elladic_image': '2.3.0.1', 'lmfdb_label': '244608.m1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 244608.m does not appear in ec_padic