Elliptic curve data - 25410.x2

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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': '25410x', 'Clabel': '25410x4', 'Cnumber': 4, 'abc_quality': 0.9822514390179332, 'absD': 14417155355562093750, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9240, 'ainvs': [1, 0, 1, -2931954, 1940712706], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 25410, 'degree': 1244160, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5222314275793832935243575180', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-1573398910560073969, 8138108343750], 'lmfdb_iso': '25410.x', 'lmfdb_label': '25410.x2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -24231, -1460289], 'min_quad_twist_disc': -11, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0.cb.1', '33.8.0-3.a.1.1', '66.24.0-6.a.1.1', '264.48.0.?', '420.24.0.?', '840.48.0.?', '1540.6.0.?', '4620.48.0.?', '9240.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.8452057438091518362695502297', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 363], [3, 4, 1694], [5, 6, 5082], [7, 8, 3630], [11, 72, 210]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3232837911801980214933857290', 'prec': 100}, 'szpiro_ratio': 5.550291359092375, '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, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 1, 4, 1, -1, 1, 0, -1, -8, -1], 'aplist': [-1, 1, -1, -1, 0, 4, 0, -8, 6, -6, -4, 8, -6, 4, 12, 6, -12, 10, -10, 0, -14, -8, 0, -12, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 25410, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '25410.x', 'trace_hash': 974383597062126368}
• 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': '0.0064449212904812799644123308673', 'prec': 110}, 'conductor': 25410, 'gens': [[42352, 8141771, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '4.8452057438091518362695502297', 'prec': 100}], 'lmfdb_label': '25410.x2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22351242170940705852039815488', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3318546779164497740919641085726452170', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-7913, 7909, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': [2, 0], '5': [1, 0], '7': [3, 0], '11': 'a', '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '25410.x2'}
• ec_torsion_growth •

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

  
  
  • id: 1280269
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '25410.x2', 'torsion': [6]}
  • id: 1280268
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [2, 2]}
  • id: 1280270
    {'degree': 4, 'field': [-216, 0, -26, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [4]}
  • id: 1280271
    {'degree': 4, 'field': [16, 0, 14, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [2, 6]}
  • id: 1280272
    {'degree': 6, 'field': [65547, -3807, -720, 485, 12, -3, 1], 'lmfdb_label': '25410.x2', 'torsion': [6]}
  • id: 1280273
    {'degree': 8, 'field': [576, 0, 37632, 0, 148, 0, -28, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [2, 4]}
  • id: 1280275
    {'degree': 8, 'field': [4096, 0, 384, 0, -248, 0, 6, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [12]}
  • id: 1280274
    {'degree': 8, 'field': [1579417, -196272, -38944, 3792, -510, -192, 32, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [2, 4]}
  • id: 1280277
    {'degree': 12, 'field': [90105, -56142, 33543, 44070, -19080, -3942, 2029, -726, 330, -110, 33, -6, 1], 'lmfdb_label': '25410.x2', 'torsion': [2, 6]}
  • id: 1280276
    {'degree': 12, 'field': [5556153, -438930, 249633, 373350, -173430, -16290, 6145, -726, 330, -110, 33, -6, 1], 'lmfdb_label': '25410.x2', 'torsion': [3, 6]}
  • id: 1280279
    {'degree': 16, 'field': [104976, 0, -1228608, 0, 3822912, 0, 1038432, 0, 79048, 0, 4656, 0, 848, 0, 24, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [2, 12]}
  • id: 1280280
    {'degree': 16, 'field': [21872752, -2171840, 7945936, -706976, 567276, 77632, -322604, 83904, -24023, 13536, 3740, -1632, 578, -160, 8, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [2, 12]}
  • id: 1280278
    {'degree': 16, 'field': [9419867136, 0, 10296456192, 0, 801536400, 0, -286266288, 0, -42910476, 0, -869792, 0, -5040, 0, -132, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [8]}
  • id: 1280281
    {'degree': 18, 'field': [50305023171648, -61475234579136, 2479175330688, 9973419193584, 1473186092112, -666281681856, -270548868324, -14266351764, 8483890968, 1746425394, -20539764, -39905082, -3047579, 361422, 54189, -1148, -378, 0, 1], 'lmfdb_label': '25410.x2', 'torsion': [18]}
• 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: 584546
    {'conductor': 25410, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '25410.x2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 584547
    {'conductor': 25410, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '25410.x2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 584548
    {'conductor': 25410, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '25410.x2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 584549
    {'conductor': 25410, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '25410.x2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 584550
    {'conductor': 25410, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '25410.x2', '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: 1833925
    {'adelic_gens': [[1550, 3, 6133, 9232], [10, 3, 4593, 9232], [11, 2, 9190, 9231], [6719, 9228, 3354, 9167], [5281, 12, 3966, 73], [1, 0, 12, 1], [9229, 12, 9228, 13], [6555, 5008, 6518, 4997], [1, 6, 6, 37], [3697, 12, 3702, 73], [1, 12, 0, 1]], 'adelic_image': '9240.96.1.?', 'conductor': 25410, 'lmfdb_label': '25410.x2', 'prime': 0}
  • id: 116112
    {'conductor': 25410, 'elladic_image': '2.3.0.1', 'lmfdb_label': '25410.x2', 'modell_image': '2B', 'prime': 2}
  • id: 116113
    {'conductor': 25410, 'elladic_image': '3.4.0.1', 'lmfdb_label': '25410.x2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1210693
    {'lmfdb_iso': '25410.x', 'p': 13, 'prec': 20, 'unit': 833472228920991710818, 'val': 1}
  • id: 1210696
    {'lmfdb_iso': '25410.x', 'p': 19, 'prec': 20, 'unit': 304667814913287594029779, 'val': 1}
  • id: 1210699
    {'lmfdb_iso': '25410.x', 'p': 23, 'prec': 20, 'unit': 38051280337201069089743133, 'val': 1}
  • id: 1210692
    {'lmfdb_iso': '25410.x', 'p': 29, 'prec': 20, 'unit': 4321310154656999122579664272, 'val': 1}
  • id: 1210703
    {'lmfdb_iso': '25410.x', 'p': 31, 'prec': 20, 'unit': 1531799933064275506701366216, 'val': 1}
  • id: 1210689
    {'lmfdb_iso': '25410.x', 'p': 37, 'prec': 20, 'unit': 488227815822257424577441676795, 'val': 1}
  • id: 1210690
    {'lmfdb_iso': '25410.x', 'p': 41, 'prec': 20, 'unit': 2179476045958583879006367276055, 'val': 1}
  • id: 1210691
    {'lmfdb_iso': '25410.x', 'p': 43, 'prec': 20, 'unit': 1847731945006926185254857120072, 'val': 1}
  • id: 1210701
    {'lmfdb_iso': '25410.x', 'p': 47, 'prec': 20, 'unit': 28318317198348204945329426959162, 'val': 1}
  • id: 1210697
    {'lmfdb_iso': '25410.x', 'p': 53, 'prec': 20, 'unit': 389693064587378763314583277118918, 'val': 1}
  • id: 1210695
    {'lmfdb_iso': '25410.x', 'p': 59, 'prec': 20, 'unit': 2923497705401607353552026579254005, 'val': 1}
  • id: 1210702
    {'lmfdb_iso': '25410.x', 'p': 61, 'prec': 20, 'unit': 5955589090967291676620374817090672, 'val': 1}
  • id: 1210688
    {'lmfdb_iso': '25410.x', 'p': 67, 'prec': 20, 'unit': 40685887767987683412968854877003651, 'val': 1}
  • id: 1210698
    {'lmfdb_iso': '25410.x', 'p': 73, 'prec': 20, 'unit': 181390979171535374436245103064474598, 'val': 1}
  • id: 1210694
    {'lmfdb_iso': '25410.x', 'p': 79, 'prec': 20, 'unit': 1167057763233374503171087853152326, 'val': 2}
  • id: 1210700
    {'lmfdb_iso': '25410.x', 'p': 89, 'prec': 20, 'unit': 1741193136797271558985176381208191250, 'val': 1}
  • id: 1210687
    {'lmfdb_iso': '25410.x', 'p': 97, 'prec': 20, 'unit': 46518070586456741255425512233930826318, 'val': 1}