Elliptic curve data - 129360.ew3

Formats: - HTML - YAML - JSON - 2025-11-05T07:01:13.836874

• 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': '129360go', 'Clabel': '129360go6', 'Cnumber': 6, 'abc_quality': 0.9961821450746233, 'absD': 1446288827061481301606400, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, 1, 0, -39691976, -76930290060], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 129360, 'degree': 15925248, 'elladic_images': ['2.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3508095631001455132260353739', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 6, 'iso_nlabel': 126, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [14351050585434661561, 3001282273281600], 'lmfdb_iso': '129360.ew', 'lmfdb_label': '129360.ew3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -50628, -3508094], 'min_quad_twist_disc': 28, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '20.12.0-2.a.1.1', '24.48.0.o.1', '60.48.0-6.a.1.2', '84.48.0.?', '120.96.0.?', '132.48.0.?', '168.96.0.?', '264.96.1.?', '308.12.0.?', '420.96.0.?', '660.96.0.?', '840.192.1.?', '924.96.0.?', '1320.192.1.?', '1540.24.0.?', '1848.192.1.?', '4620.192.1.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.8222170269110238859080098795', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 3920], [5, 6, 25872], [7, 32, 2640], [11, 12, 11760]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6847073080125435512561268807', 'prec': 100}, 'szpiro_ratio': 5.446189570357341, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, 0, 0, 1, 0, 1, 0, -2, 0, -1, 0, -6, 0, -4, 0], 'aplist': [0, 1, -1, 0, 1, -2, -6, -4, 0, 6, -4, 2, -6, 4, 0, 6, 0, -2, 4, 0, -2, -8, 12, -6, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 129360, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '129360.ew', 'trace_hash': 325547888961197881}
• 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': '0.0012289205135518104973345715859', 'prec': 110}, 'conductor': 129360, 'gens': [[-3938, 135360, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.8222170269110238859080098795', 'prec': 100}], 'lmfdb_label': '129360.ew3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.061035776155258900414142128037', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.0638662166388641356997608493723611648', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[-2210, 0, 1], [7107, 0, 1]], 'xcoord_integral_points': [-4898, -3938, -2210, 7107, 28716]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 1], '5': [1, 0], '7': 'a', '11': [2, 0], '13': [1, 0], '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': '129360.ew3'}
• ec_torsion_growth •

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

  
  
  • id: 5881262
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 6]}
  • id: 5881265
    {'degree': 4, 'field': [324, 0, -41, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 4]}
  • id: 5881263
    {'degree': 4, 'field': [729, 0, 12, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 4]}
  • id: 5881264
    {'degree': 4, 'field': [1369, 0, 94, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 4]}
  • id: 5881266
    {'degree': 6, 'field': [-118, -630, 147, -30, -21, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 6]}
  • id: 5881268
    {'degree': 8, 'field': [1684, 940, -214, -1502, 877, -154, 56, -4, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 12]}
  • id: 5881269
    {'degree': 8, 'field': [2116, 0, -12, 0, 173, 0, 18, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 12]}
  • id: 5881267
    {'degree': 8, 'field': [39204, 0, 1980, 0, 421, 0, -32, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 12]}
  • id: 5881270
    {'degree': 12, 'field': [13924, -74340, 414246, 99690, 231, 30870, 3751, 0, 294, -60, 21, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [6, 6]}
  • id: 5881274
    {'degree': 16, 'field': [-339452739, 4529491896, -2444388124, -3961464976, 1467876118, 590541256, -156303456, -32908008, 5975383, 1419496, -203784, -41848, 5458, 672, -76, -8, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 8]}
  • id: 5881271
    {'degree': 16, 'field': [924004, 2541240, 2072100, 974808, 5495602, -1546344, 3091050, -436968, 483261, -77220, 1710, -432, 1480, -108, 12, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [4, 4]}
  • id: 5881273
    {'degree': 16, 'field': [12642528721, 0, 8800761544, 0, 1483387972, 0, 46200232, 0, -123050, 0, 337528, 0, 292, 0, -104, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 8]}
  • id: 5881272
    {'degree': 16, 'field': [266479991089, 0, -30940482080, 0, 4672940236, 0, -3328832, 0, 9826006, 0, -95264, 0, 4396, 0, -128, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 8]}
  • id: 5881275
    {'degree': 18, 'field': [4928721265048896, -1207338424959744, 186142424388480, 46056640912128, -4803562972656, -2776897414368, 147042691776, 43918459200, 8766548676, 2596116600, 609617556, 50195376, 3416505, 399168, 42039, -1848, -369, 0, 1], 'lmfdb_label': '129360.ew3', 'torsion': [2, 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: 3189825
    {'conductor': 129360, 'conductor_valuation': 4, 'discriminant_valuation': 18, 'j_denominator_valuation': 6, 'kodaira_symbol': -14, 'lmfdb_label': '129360.ew3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3189826
    {'conductor': 129360, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '129360.ew3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3189827
    {'conductor': 129360, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '129360.ew3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3189828
    {'conductor': 129360, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '129360.ew3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3189829
    {'conductor': 129360, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '129360.ew3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2506632
    {'adelic_gens': [[2521, 12, 5886, 73], [9, 4, 9224, 9233], [4621, 6, 0, 1], [9233, 9234, 3966, 5], [1, 0, 12, 1], [9229, 12, 9228, 13], [6161, 6, 1540, 1], [7399, 6, 5538, 9235], [1, 12, 0, 1], [6929, 9228, 0, 9239]], 'adelic_image': '9240.384.5.?', 'conductor': 129360, 'lmfdb_label': '129360.ew3', 'prime': 0}
  • id: 503716
    {'conductor': 129360, 'elladic_image': '2.6.0.1', 'lmfdb_label': '129360.ew3', 'modell_image': '2Cs', 'prime': 2}
  • id: 503717
    {'conductor': 129360, 'elladic_image': '3.4.0.1', 'lmfdb_label': '129360.ew3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 6784134
    {'lmfdb_iso': '129360.ew', 'p': 13, 'prec': 20, 'unit': 1342141003558947640248, 'val': 1}
  • id: 6784136
    {'lmfdb_iso': '129360.ew', 'p': 17, 'prec': 20, 'unit': 8702673648554602901086, 'val': 1}
  • id: 6784127
    {'lmfdb_iso': '129360.ew', 'p': 19, 'prec': 20, 'unit': 817317970410351539510228, 'val': 1}
  • id: 6784133
    {'lmfdb_iso': '129360.ew', 'p': 29, 'prec': 20, 'unit': 4909874345181508745962605367, 'val': 1}
  • id: 6784142
    {'lmfdb_iso': '129360.ew', 'p': 31, 'prec': 20, 'unit': 1011389518700228785928071860, 'val': 1}
  • id: 6784130
    {'lmfdb_iso': '129360.ew', 'p': 37, 'prec': 20, 'unit': 325966546519420616573178141281, 'val': 1}
  • id: 6784131
    {'lmfdb_iso': '129360.ew', 'p': 41, 'prec': 20, 'unit': 787947723144239005271338128544, 'val': 1}
  • id: 6784132
    {'lmfdb_iso': '129360.ew', 'p': 43, 'prec': 20, 'unit': 10375210333602192116950541561793, 'val': 1}
  • id: 6784138
    {'lmfdb_iso': '129360.ew', 'p': 53, 'prec': 20, 'unit': 369537044943179084656135105515450, 'val': 1}
  • id: 6784141
    {'lmfdb_iso': '129360.ew', 'p': 61, 'prec': 20, 'unit': 8012669579744807679299833141669649, 'val': 1}
  • id: 6784129
    {'lmfdb_iso': '129360.ew', 'p': 67, 'prec': 20, 'unit': 19217643621680585977973181428794813, 'val': 1}
  • id: 6784139
    {'lmfdb_iso': '129360.ew', 'p': 73, 'prec': 20, 'unit': 2218043220210000724653532762334613, 'val': 2}
  • id: 6784135
    {'lmfdb_iso': '129360.ew', 'p': 79, 'prec': 20, 'unit': 189467877428083930409611173059596405, 'val': 1}
  • id: 6784137
    {'lmfdb_iso': '129360.ew', 'p': 83, 'prec': 20, 'unit': 2508286671514331183876320718352080571, 'val': 1}
  • id: 6784140
    {'lmfdb_iso': '129360.ew', 'p': 89, 'prec': 20, 'unit': 9801834768236644994048821415357333892, 'val': 1}
  • id: 6784128
    {'lmfdb_iso': '129360.ew', 'p': 97, 'prec': 20, 'unit': 31935459937372427176778514102914201536, 'val': 1}