{
  "id": 4266,
  "curve_key": "26337917457832194826038351747249119056:-123409569559168037252810254520772941414880745883652704704",
  "ainvs": [
    "0",
    "1",
    "0",
    "-548706613704837392209132328067689980",
    "142835149952740783674517071497430292197512309490923600"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 258.4922189313343,
  "faltings_height": 19.507860727013256,
  "conductor": "83649190332021251463700004192640613044692062259091513678741325837066688815236766833685048440",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "29",
    "139",
    "157",
    "241",
    "8998992345821347",
    "650595954117933225616883",
    "70966449329823133133861281900953128449561"
  ],
  "discriminant": "1759444451470850072684319011374877786144475600337765331769711640725368876180306924429916745456646917812000000",
  "regulator": "151860770353785919699884861.3734098434605305872601080008700546279278480960188578065477136",
  "points": [
    [
      "-322612288266463310",
      "-535049140095720417696030150"
    ],
    [
      "15101961994925738978",
      "58618678989712271461800699114"
    ],
    [
      "907836714828363740",
      "-626824263049991300346669900"
    ],
    [
      "273556730485214915",
      "114908273991395956396567800"
    ],
    [
      "181946630301187352090",
      "-2454214010398981472388802794750"
    ],
    [
      "4405724565203813290",
      "9123721852952122916335842450"
    ],
    [
      "294607625691332570",
      "-82170976369137785009752770"
    ],
    [
      "-313294585885923460",
      "532908061394753138675199300"
    ],
    [
      "199624270423481390",
      "203113243331835429005051550"
    ],
    [
      "6717774573282858590",
      "17309529326775121999091604750"
    ],
    [
      "8201454527851561015",
      "-23394531459613302805642843050"
    ],
    [
      "124398187208413790",
      "276590116459375384811489550"
    ],
    [
      "-703025779009966960",
      "425585356236238734257865300"
    ],
    [
      "1789232560467106640",
      "2211116621489700873125829300"
    ],
    [
      "-670557120399732010",
      "-457449864682014966319633350"
    ],
    [
      "15680328286312688510/49",
      "1346710056133300259165712450/343"
    ],
    [
      "304605923857901980",
      "62917844794054052046552660"
    ],
    [
      "183115357750036355",
      "-220224036015020076678159840"
    ],
    [
      "-824064662148353581",
      "188140728491421236396742060"
    ],
    [
      "-590506366020979229710/841",
      "10403023673830024705152948375150/24389"
    ],
    [
      "1079154265398875525/4",
      "961238366486162419140130095/8"
    ],
    [
      "-71189382008228890",
      "426070947162502862745060330"
    ],
    [
      "-24351529057095010",
      "-395199385901991852532873650"
    ],
    [
      "527276687781423740",
      "-10429805063143987643420100"
    ],
    [
      "4252941516679212954770/19321",
      "485786989200385305513145137345570/2685619"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -153/175 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -6276238998830220029652T^8 - 147117265740737393263056T^7 - 1476608115021273186431436T^6 - 2537588378961323810084232T^5 - 2548792821173728264463880T^4 - 1085007595485857335267392T^3 + 1266527474226087852521664T^2 + 648517828968568984999104T - 394596892599474187722672,\nA6 = 183805362097981758392518604760804T^12 + 5732624758080384420828430168047168T^11 + 73959871695264874512454632891659784T^10 + 444783553219225017837165953570627520T^9 + 2344794983173561552804045815952068900T^8 + 3952769116759113473247850984388751264T^7 + 1034132030293362061211853414656889168T^6 - 2105709468706045084822083295783288416T^5 - 399200243459621989020610997025954720T^4 + 954359071876325078141973753377053440T^3 - 120506571390369672930568955416602624T^2 - 234913768366312396616401364230326528T + 83823186438658476366371918607332736.\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 23:17:44",
  "updated_at": "2026-10-15 23:17:44"
}