{
  "id": 4233,
  "curve_key": "19103710846821535960122787018060512976:-92882926533326161341536760474458574292340369374256300224",
  "ainvs": [
    "0",
    "1",
    "0",
    "-397993975975448665835891396209594020",
    "107503387191349723642262147446214535337504221372561600"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 257.7418697346569,
  "faltings_height": 19.45152073449741,
  "conductor": "5227522119347253134367698504405002351684899917802529603902390934965733498909951087093080",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "31",
    "43",
    "79",
    "89",
    "994489",
    "8830452193",
    "2554614859020113",
    "48790382850554741353",
    "1092471856440567451788553"
  ],
  "discriminant": "-957931128596215762462972924449444131268846999209717221848474201804550816440881935376185193710551807708000000",
  "regulator": "12344453430040317632674191.751109999265547187778819639975393075165414805258636155359798",
  "points": [
    [
      "382274873004612735",
      "-105941856132035394619209750"
    ],
    [
      "-733762256661954090",
      "66884778856483122824149050"
    ],
    [
      "-217075561574575440",
      "428566403203999761416398800"
    ],
    [
      "-127482891993540257760/289",
      "-2181896671716575570062094747400/4913"
    ],
    [
      "-209440004917830540",
      "-426230146091717708928275400"
    ],
    [
      "56457669740665525920/121",
      "-203532125972948670858927936840/1331"
    ],
    [
      "-1436865894430989435/4",
      "3614347872789281464563572625/8"
    ],
    [
      "235317344242179060",
      "163948235057282387870098200"
    ],
    [
      "334926039987568683",
      "-108514150638656934136947696"
    ],
    [
      "352788686940847110",
      "-104898259032038671348790250"
    ],
    [
      "565023529184220660",
      "-251022081780753881859586200"
    ],
    [
      "4377057159736170790/9",
      "4595971302249639624628251650/27"
    ],
    [
      "316773329294558448",
      "-114961900189726413641430144"
    ],
    [
      "-326994002478031950",
      "-450201256383742579972880910"
    ],
    [
      "1698803943645516660",
      "2081832638989456422477649800"
    ],
    [
      "-404342776091064690",
      "-449802323507323780638354450"
    ],
    [
      "-630350257745993040",
      "328503742325074800617000400"
    ],
    [
      "14657163847995806865/64",
      "-86234205952039758455250231975/512"
    ],
    [
      "1060008195356799810",
      "936306646391565091687763550"
    ],
    [
      "430226640028340640",
      "126129138794453642145241320"
    ],
    [
      "-591149707063693920",
      "-369046649169741442258592280"
    ],
    [
      "110995449378270075",
      "254352766409911677367036260"
    ],
    [
      "36919739458863247365/4",
      "-223821052069886825357634540975/8"
    ],
    [
      "12122605872548589435",
      "42152004916174281232237001700"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 282/31 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -197025213169039645478907T^8 - 341931841726476599360316T^7 + 665947206984249248496984T^6 + 768079108867411834646148T^5 - 206522586961384218063030T^4 + 567964478469951746923788T^3 - 1467887770507529603462256T^2 - 589605913192300591575636T - 60265701752223364133607,\nA6 = 36494962374013345038748480651016406T^12 + 110908265109200423180608249500271092T^11 - 159142246935958461715703643687536484T^10 - 720270176428343092357105513183159380T^9 + 221065402893902851082492835239899950T^8 + 1953863404097225126588131072937056920T^7 - 202924758161403130921394088084358680T^6 - 2477568108201452732342173930140320280T^5 + 261194239478925852479287144045333650T^4 + 771382032898538394406350724439690100T^3 + 379387733802661108189747796000121180T^2 + 80405723305695990012919388855834220T + 5982031282168624025426587018231050.\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 02:59:30",
  "updated_at": "2026-10-15 02:59:30"
}