Elliptic curve data - 121680.e7

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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': '121680dz', 'Clabel': '121680dz3', 'Cnumber': 3, 'abc_quality': 1.0491971880149842, 'absD': 22138021547606016000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -329043, -237746158], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 2654208, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3959468082811748940136086608', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-273359449, 1536000], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -14, -64], 'min_quad_twist_disc': 156, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.1', '24.96.1.dh.4', '30.24.0.b.1', '40.12.0.bb.1', '52.12.0-4.c.1.1', '60.96.1.n.2', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '780.192.1.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.993925787616846496861917737', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 7605], [3, 8, 2704], [5, 6, 24336], [13, 86, 720]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.12898119534359362912798979990', 'prec': 107}, 'szpiro_ratio': 4.449219120222503, '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, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, -1, -4, 0, 0, -6, -4, 0, 6, 8, -2, -6, 4, 0, 6, 0, -10, -4, 0, -2, -8, -12, 18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 121680, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '121680.e', 'trace_hash': 1750704086879226857}
• 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': '0.0082967316688852978439989319796', 'prec': 110}, 'conductor': 121680, 'gens': [[1673897, 2121512960, 23]], 'heights': [{'__RealLiteral__': 0, 'data': '10.993925787616846496861917737', 'prec': 100}], 'lmfdb_label': '121680.e7', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.089456881067086070503853511413', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9339292465728431646689618320141460064', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[793, 0, 1]], 'xcoord_integral_points': [793]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '121680.e7'}
• ec_torsion_growth •

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

  
  
  • id: 5557607
    {'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [4]}
  • id: 5557606
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '121680.e7', 'torsion': [2, 2]}
  • id: 5557608
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [12]}
  • id: 5557609
    {'degree': 4, 'field': [94, -34, 35, -2, 1], 'lmfdb_label': '121680.e7', 'torsion': [2, 12]}
  • id: 5557610
    {'degree': 6, 'field': [-6591, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [6]}
  • id: 5557611
    {'degree': 8, 'field': [771, -492, 576, -156, 49, 32, -6, -4, 1], 'lmfdb_label': '121680.e7', 'torsion': [2, 4]}
  • id: 5557613
    {'degree': 8, 'field': [54136, -11456, 12404, -1940, 1081, -136, 50, -4, 1], 'lmfdb_label': '121680.e7', 'torsion': [24]}
  • id: 5557612
    {'degree': 8, 'field': [175366, 30948, -28814, -4196, 1919, 212, -66, -4, 1], 'lmfdb_label': '121680.e7', 'torsion': [8]}
  • id: 5557614
    {'degree': 12, 'field': [4813636, 0, 2242968, 0, 427245, 0, 43946, 0, 2535, 0, 78, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [3, 12]}
  • id: 5557616
    {'degree': 12, 'field': [43322644, 435012, -692046, 527270, -296625, 39552, -13141, -6, -30, 10, 9, -6, 1], 'lmfdb_label': '121680.e7', 'torsion': [12]}
  • id: 5557615
    {'degree': 12, 'field': [57913704, 0, 0, 518508, 0, 0, 21813, 0, 0, -216, 0, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [2, 6]}
  • id: 5557617
    {'degree': 16, 'field': [14641, 0, 6636, 0, 79090, 0, -37476, 0, 11379, 0, -1836, 0, 250, 0, -24, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [4, 12]}
  • id: 5557619
    {'degree': 16, 'field': [378847296, 0, 340092864, 0, 117982848, 0, 20775096, 0, 2148673, 0, 136552, 0, 5262, 0, 112, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [2, 24]}
  • id: 5557618
    {'degree': 16, 'field': [1475789056, 0, -67765824, 0, -708295, 0, 1764, 0, -60861, 0, -1656, 0, 395, 0, 36, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [2, 24]}
  • id: 5557620
    {'degree': 18, 'field': [13178301152, 4150679520, 9761599536, 1845897760, 3063158280, 324817800, 520017332, 29282160, 53707704, 1286660, 3652644, 15360, 172033, -720, 5571, -20, 111, 0, 1], 'lmfdb_label': '121680.e7', 'torsion': [36]}
• 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: 2995183
    {'conductor': 121680, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '121680.e7', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2995184
    {'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '121680.e7', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2995185
    {'conductor': 121680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '121680.e7', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2995186
    {'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121680.e7', 'prime': 13, 'reduction_type': 0, '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: 2457884
    {'adelic_gens': [[1104, 247, 169, 246], [352, 1443, 117, 274], [1, 12, 12, 145], [1537, 24, 1536, 25], [479, 0, 0, 1559], [623, 936, 1326, 1169], [15, 106, 254, 131], [1, 24, 0, 1], [729, 988, 260, 989], [1, 0, 24, 1]], 'adelic_image': '1560.384.5.?', 'conductor': 121680, 'lmfdb_label': '121680.e7', 'prime': 0}
  • id: 477396
    {'conductor': 121680, 'elladic_image': '4.6.0.1', 'lmfdb_label': '121680.e7', 'modell_image': '2B', 'prime': 2}
  • id: 477397
    {'conductor': 121680, 'elladic_image': '3.4.0.1', 'lmfdb_label': '121680.e7', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 6361699
    {'lmfdb_iso': '121680.e', 'p': 7, 'prec': 20, 'unit': 3655126417512847, 'val': 1}
  • id: 6361704
    {'lmfdb_iso': '121680.e', 'p': 17, 'prec': 20, 'unit': 157486403324793425271999, 'val': 1}
  • id: 6361695
    {'lmfdb_iso': '121680.e', 'p': 19, 'prec': 20, 'unit': 1465719948403277590253664, 'val': 1}
  • id: 6361702
    {'lmfdb_iso': '121680.e', 'p': 29, 'prec': 20, 'unit': 1210003974022209909380232618, 'val': 1}
  • id: 6361710
    {'lmfdb_iso': '121680.e', 'p': 31, 'prec': 20, 'unit': 519916441349091585730491626, 'val': 1}
  • id: 6361698
    {'lmfdb_iso': '121680.e', 'p': 37, 'prec': 20, 'unit': 320824555419521225653657006687, 'val': 1}
  • id: 6361700
    {'lmfdb_iso': '121680.e', 'p': 41, 'prec': 20, 'unit': 1006818582697798013754455184026, 'val': 1}
  • id: 6361701
    {'lmfdb_iso': '121680.e', 'p': 43, 'prec': 20, 'unit': 154738038948532199300645832436, 'val': 1}
  • id: 6361706
    {'lmfdb_iso': '121680.e', 'p': 53, 'prec': 20, 'unit': 434237483939887250325972754640005, 'val': 1}
  • id: 6361709
    {'lmfdb_iso': '121680.e', 'p': 61, 'prec': 20, 'unit': 6444350278983481418665141482497898, 'val': 1}
  • id: 6361697
    {'lmfdb_iso': '121680.e', 'p': 67, 'prec': 20, 'unit': 22832319830563244966439552818854775, 'val': 1}
  • id: 6361707
    {'lmfdb_iso': '121680.e', 'p': 73, 'prec': 20, 'unit': 20544479874469637442433102095691288, 'val': 1}
  • id: 6361703
    {'lmfdb_iso': '121680.e', 'p': 79, 'prec': 20, 'unit': 195501196714420863351160941671496151, 'val': 1}
  • id: 6361705
    {'lmfdb_iso': '121680.e', 'p': 83, 'prec': 20, 'unit': 796565802152685252515251970240006901, 'val': 1}
  • id: 6361708
    {'lmfdb_iso': '121680.e', 'p': 89, 'prec': 20, 'unit': 2976206864814925705708995924057961043, 'val': 1}
  • id: 6361696
    {'lmfdb_iso': '121680.e', 'p': 97, 'prec': 20, 'unit': 43208109913718632311793379341079283355, 'val': 1}