{
  "id": 4234,
  "curve_key": "4190940526151241831686019750162205246561:-312000216479128438437546249271902737837615990946517005089809",
  "ainvs": [
    "1",
    "0",
    "0",
    "-87311260961484204826792078128379275970",
    "361111361665657914850995183429023003576489538566289001412"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 273.9807083646264,
  "faltings_height": 20.817253003666437,
  "conductor": "58219598583889402267386060059408058903194768838964817551390692790917204922228640375910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "83",
    "97",
    "139",
    "11617",
    "278491",
    "4317816702373",
    "80316743721719",
    "118776478958706660989128744648406799289"
  ],
  "discriminant": "-13735259866556888673444576442144357662758639946498113227088464928848250077159178701215696442846163744369869824000000",
  "regulator": "3041973519286326786080174.8323011709909848504638720602552896286655746527771314978561530",
  "points": [
    [
      "-4693227481740211036",
      "25836178888676683699093828718"
    ],
    [
      "37581531059750504204",
      "223961833825845210489921673958"
    ],
    [
      "7116346323032784644",
      "-10008143736117182275074210802"
    ],
    [
      "6937879390984378214",
      "9450155167987489328409042818"
    ],
    [
      "6278674593843288014",
      "-7773592165697177684625203632"
    ],
    [
      "11402158614586750514",
      "-29119757480090846177575378132"
    ],
    [
      "-10951694666097647266",
      "1943084969116608638492552738"
    ],
    [
      "5381326263004597514",
      "-6862728618224852494712784382"
    ],
    [
      "-5784687579082348636",
      "25934706127905821560979956718"
    ],
    [
      "9070440000156921764",
      "-17759815480804799985694804882"
    ],
    [
      "-911310000510532336",
      "-20974321366767892116515469682"
    ],
    [
      "24778525165209201764",
      "-115806173157827573850981244882"
    ],
    [
      "39695715021529387331/4",
      "-173803092260204651728843229381/8"
    ],
    [
      "6794099022214461764",
      "-9029071686268296904144024882"
    ],
    [
      "-6182923758107481436",
      "25779566424691599622349639918"
    ],
    [
      "66784699504235272664",
      "-540742924622746314677523729682"
    ],
    [
      "-513899506230609023164/49",
      "-3807658561951858761956743012126/343"
    ],
    [
      "4205005179848064164",
      "8265606264802432300248993518"
    ],
    [
      "-8845907921848133836",
      "-21006324579629607812579894482"
    ],
    [
      "-1046391139169601557752/841",
      "-527513170772513988811388058509006/24389"
    ],
    [
      "-677556879794204956",
      "-20492892722459646878493634642"
    ],
    [
      "3506518875130245044",
      "9902918367901619468179789598"
    ],
    [
      "157450003582410538984964/32761",
      "42965190208478117168733057582683798/5929741"
    ],
    [
      "13080938904552169028",
      "38174469725741615838927509966"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1072/239 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -9326637192413076012400T^8 - 34884996069313200087200T^7 + 110925288656556862233440T^6 + 385813899399942596207360T^5 + 233890070443452935336560T^4 - 596691564815170847368240T^3 - 9841086512215258337654200T^2 - 7147300944594901868231960T - 1372341018983665060065307,\nA6 = 355645975300077069151201411600000T^12 + 2273247912229167049862154805705600T^11 - 7137338446733984479207110102193984T^10 - 57261816964678192543182240688567360T^9 + 101108657979008556764293700373699600T^8 + 692858910748462408271944263396908640T^7 - 1034224818521729452686537198181505760T^6 - 4446809343349652848812523474435426752T^5 + 4366238810355442164044492645139162240T^4 + 13060804253335292158409237965744231280T^3 + 12512018819180205106449295745222847800T^2 + 4777750191287146089865021403646408520T + 622816136791651503989297338315313206.\nIt is a 2-neighbour of the fibration given in curve#3900: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-15 03:24:33",
  "updated_at": "2026-10-15 03:24:33"
}