Elliptic curve data - 9240.m5

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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': '9240u', 'Clabel': '9240u1', 'Cnumber': 1, 'abc_quality': 0.9204368882924238, 'absD': 15881250000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 18480, 'ainvs': [0, -1, 0, -1055, 12072], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 9240, 'degree': 8192, 'elladic_images': ['8.24.0.45'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.68764132910482666790845033436', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [8124052043776, 992578125], 'lmfdb_iso': '9240.m', 'lmfdb_label': '9240.m5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1055, 12072], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.2', '42.6.0.a.1', '80.48.0.?', '84.24.0.?', '88.48.0.?', '168.48.0.?', '880.96.0.?', '1680.96.0.?', '1848.96.0.?', '18480.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 21], [3, 4, 3080], [5, 6, 1848], [7, 8, 1320], [11, 12, 840]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.45659226891817823143603962721', 'prec': 103}, 'szpiro_ratio': 3.5590166766124143, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 0, 6, 0, -1, 0, 2, 0, 4, 0], 'aplist': [0, -1, 1, -1, 1, 6, 2, 4, 8, -2, 8, 6, -6, -4, 8, 6, -12, 14, -4, 0, -6, 0, -12, -6, -6], 'class_deg': 8, 'class_size': 6, 'conductor': 9240, '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': '9240.m', 'trace_hash': 867577008702740865}
• 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': '0.25276813871670888025571501191', 'prec': 103}, 'conductor': 9240, 'gens': [], 'heights': [], 'lmfdb_label': '9240.m5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1974765245741271667825908268', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3949530491482543335651816536304262882', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[49, 275, 1]], 'xcoord_integral_points': [24, 49]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [1, 0], '7': [0, 0], '11': [3, 0]}, 'iwp0': 3, 'lmfdb_label': '9240.m5'}
• ec_torsion_growth •

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

  
  
  • id: 480251
    {'degree': 2, 'field': [-231, 0, 1], 'lmfdb_label': '9240.m5', 'torsion': [8]}
  • id: 480252
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '9240.m5', 'torsion': [8]}
  • id: 480250
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '9240.m5', 'torsion': [2, 4]}
  • id: 480253
    {'degree': 4, 'field': [25, 32, -31, -2, 1], 'lmfdb_label': '9240.m5', 'torsion': [2, 8]}
  • id: 480256
    {'degree': 8, 'field': [-2084375, -11172500, -530500, 574300, 44410, -7300, -796, -4, 1], 'lmfdb_label': '9240.m5', 'torsion': [16]}
  • id: 480258
    {'degree': 8, 'field': [-3, 0, 7048, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '9240.m5', 'torsion': [12]}
  • id: 480255
    {'degree': 8, 'field': [25, 10, 2, -26, 19, -10, 8, -4, 1], 'lmfdb_label': '9240.m5', 'torsion': [2, 8]}
  • id: 480257
    {'degree': 8, 'field': [275000, 220000, 66000, 8800, 540, 40, -16, -4, 1], 'lmfdb_label': '9240.m5', 'torsion': [16]}
  • id: 480254
    {'degree': 8, 'field': [403225, 1270, 2, -2546, 1279, -10, 8, -4, 1], 'lmfdb_label': '9240.m5', 'torsion': [4, 4]}
  • id: 480259
    {'degree': 16, 'field': [36100, 0, -48864, 0, 14164, 0, -3348, 0, 2973, 0, 1188, 0, 262, 0, 24, 0, 1], 'lmfdb_label': '9240.m5', 'torsion': [4, 8]}
  • id: 480262
    {'degree': 16, 'field': [3515625, 0, 30736200, 0, -6332450, 0, 884400, 0, 11127, 0, -352, 0, -426, 0, 0, 0, 1], 'lmfdb_label': '9240.m5', 'torsion': [2, 12]}
  • id: 480264
    {'degree': 16, 'field': [2750000000, 2200000000, -1430000000, -1386000000, -367400000, -23320000, 10240000, -344000, -1416000, 228400, 112280, -8272, -1636, 84, 8, -8, 1], 'lmfdb_label': '9240.m5', 'torsion': [24]}
  • id: 480261
    {'degree': 16, 'field': [7750125625, -13271098500, 9716227400, 2416091700, -1137672470, 256318480, 5375744, -23606220, 8332083, -1037704, 109808, -31340, 6230, -188, -16, -8, 1], 'lmfdb_label': '9240.m5', 'torsion': [2, 16]}
  • id: 480260
    {'degree': 16, 'field': [2954101562500, 4726562500000, 2268750000000, -132343750000, -425493750000, -97680000000, 12223750000, 6945125000, 372000000, -146888000, -17531600, 838800, 176520, -560, -696, -4, 1], 'lmfdb_label': '9240.m5', 'torsion': [2, 16]}
  • id: 480263
    {'degree': 16, 'field': [116825596170921, 0, -9654708980268, 0, 612726085708, 0, -23231727156, 0, 651386670, 0, -12059476, 0, 124188, 0, -588, 0, 1], 'lmfdb_label': '9240.m5', 'torsion': [24]}
• 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: 193741
    {'conductor': 9240, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '9240.m5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 193742
    {'conductor': 9240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9240.m5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 193743
    {'conductor': 9240, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '9240.m5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 193744
    {'conductor': 9240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9240.m5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 193745
    {'conductor': 9240, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '9240.m5', 'prime': 11, '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: 1725031
    {'adelic_gens': [[1, 16, 0, 1], [18465, 16, 18464, 17], [1, 16, 13860, 13861], [15, 2, 18382, 18467], [6176, 5, 18435, 18466], [3697, 16, 11096, 129], [5053, 16, 1424, 18165], [5, 4, 18476, 18477], [1, 0, 16, 1], [10576, 5, 2595, 18466], [11565, 16, 16394, 4859]], 'adelic_image': '18480.192.1.?', 'conductor': 9240, 'lmfdb_label': '9240.m5', 'prime': 0}
  • id: 44846
    {'conductor': 9240, 'elladic_image': '8.24.0.45', 'lmfdb_label': '9240.m5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 9240.m does not appear in ec_padic