Elliptic curve data - 15680.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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '15680u', 'Clabel': '15680u2', 'Cnumber': 2, 'abc_quality': 0.9862214437483838, 'absD': 18512297918464000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 840, 'ainvs': [0, 1, 0, -1539841, 734980959], 'analytic_rank': 0, 'bad_primes': [2, 5, 7], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 15680, 'degree': 241920, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1970644581604094518512989117', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 3], 'jinv': [-5452947409, 250], 'lmfdb_iso': '15680.m', 'lmfdb_label': '15680.m1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -491, -4229], 'min_quad_twist_disc': -56, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '40.2.0.a.1', '120.8.0.?', '168.8.0.?', '420.8.0.?', '840.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 245], [3, 2, 3136], [5, 6, 3136], [7, 20, 320]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.46424810355893626652900989002', 'prec': 107}, 'szpiro_ratio': 5.626755387463219, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, 0, -1, 0, 0, 0, 1, 0, -3, 0, 5, 0, 2, 0, -6, 0, -1, 0], 'aplist': [0, -2, -1, 0, -3, 5, -6, -1, 3, 6, 4, -11, -3, 10, -3, -3, 0, -4, 4, 12, 4, -10, -12, -6, -14], 'class_deg': 3, 'class_size': 2, 'conductor': 15680, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '15680.m', 'trace_hash': 1977105497764587148}
• 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': '0.012349633205350552719108680110', 'prec': 107}, 'conductor': 15680, 'gens': [], 'heights': [], 'lmfdb_label': '15680.m1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.36448921588428011708640812613', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.72897843176856023417281625225669158446', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [0, 0], '7': 'a', '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '15680.m1'}
• ec_torsion_growth •

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

  
  
  • id: 805309
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '15680.m1', 'torsion': [3]}
  • id: 805310
    {'degree': 3, 'field': [15, 5, -1, 1], 'lmfdb_label': '15680.m1', 'torsion': [2]}
  • id: 805313
    {'degree': 6, 'field': [-1512, 0, 441, 0, -42, 0, 1], 'lmfdb_label': '15680.m1', 'torsion': [6]}
  • id: 805312
    {'degree': 6, 'field': [14, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '15680.m1', 'torsion': [3]}
  • id: 805311
    {'degree': 6, 'field': [90, 0, 61, 0, 8, 0, 1], 'lmfdb_label': '15680.m1', 'torsion': [2, 2]}
  • id: 805315
    {'degree': 12, 'field': [225, -90, -189, 510, -120, -210, 169, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '15680.m1', 'torsion': [3, 3]}
  • id: 805314
    {'degree': 12, 'field': [27392, -2048, -18538, 17146, -7774, 1124, 1218, -838, 174, -32, 13, -1, 1], 'lmfdb_label': '15680.m1', 'torsion': [4]}
  • id: 805316
    {'degree': 12, 'field': [2566404, 0, -1278072, 0, 291708, 0, -23820, 0, 1297, 0, -52, 0, 1], 'lmfdb_label': '15680.m1', 'torsion': [2, 6]}
  • id: 805317
    {'degree': 18, 'field': [-284794272, 0, 2115508752, 0, 219547440, 0, 171421012, 0, -26146008, 0, 2327304, 0, -120134, 0, 3780, 0, -84, 0, 1], 'lmfdb_label': '15680.m1', 'torsion': [9]}
  • id: 805318
    {'degree': 18, 'field': [11543176, 0, 0, -3023200, 0, 0, 446436, 0, 0, -35888, 0, 0, 1234, 0, 0, -24, 0, 0, 1], 'lmfdb_label': '15680.m1', 'torsion': [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: 347296
    {'conductor': 15680, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '15680.m1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 347297
    {'conductor': 15680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '15680.m1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 347298
    {'conductor': 15680, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '15680.m1', 'prime': 7, 'reduction_type': 0, '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: 1768503
    {'adelic_gens': [[4, 3, 9, 7], [835, 6, 834, 7], [419, 714, 777, 461], [218, 147, 175, 547], [599, 0, 0, 839], [337, 126, 651, 379], [1, 6, 0, 1], [3, 4, 8, 11], [631, 126, 693, 379], [1, 0, 6, 1]], 'adelic_image': '840.16.0.?', 'conductor': 15680, 'lmfdb_label': '15680.m1', 'prime': 0}
  • id: 73944
    {'conductor': 15680, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15680.m1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 15680.m does not appear in ec_padic