{
  "id": 4557,
  "curve_key": "520932074691607773722381177760106557376:-10798230826296729613142135801576771641512378620253053781376",
  "ainvs": [
    "0",
    "1",
    "0",
    "-10852751556075161952549607870002219945",
    "12497952345250844456037665918318431712011680038995850043"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 267.4460490185019,
  "faltings_height": 20.25670852733072,
  "conductor": "143917957977217058693436268679010221745477195815652119315932364093686471734960924840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "61",
    "67",
    "71",
    "103",
    "66387491",
    "21682994323693",
    "68663616677926063",
    "1458412826058344054194326737477"
  ],
  "discriminant": "14330825284860788285747106080655833798875070037187364094619187516440697344698819568822963764944539150577076000000",
  "regulator": "189203803055899682250529.07190687929349625278628735187204577856446334405072608822638203",
  "points": [
    [
      "1389741727266657291",
      "315520053265366645573880730"
    ],
    [
      "909508178723125053",
      "1838378598653703880671863238"
    ],
    [
      "2512205040831294531",
      "1043349766635514852137093750"
    ],
    [
      "-690511658695149219",
      "-4434260195283940606991883750"
    ],
    [
      "-3389866291190140989",
      "3214610336428879164963829110"
    ],
    [
      "22955287873232819631",
      "108901559330513463709686213450"
    ],
    [
      "-84905453131330669",
      "3663167762451770448944400150"
    ],
    [
      "-1730935736894895459",
      "-5108546232661807045904296230"
    ],
    [
      "-1860314779053008619",
      "-5123413205729398661423274450"
    ],
    [
      "2550080447835273243",
      "1185540881853736405728152058"
    ],
    [
      "5054553551074042579/9",
      "69259097976167049826279275550/27"
    ],
    [
      "2444988868107404691",
      "761030280622267880396829930"
    ],
    [
      "779680791155607231",
      "-2123732573610018702001684650"
    ],
    [
      "10899383870841506931",
      "34482155567451618611116718550"
    ],
    [
      "2836996960182651471",
      "-2131301486319493964124782070"
    ],
    [
      "10632960820643331549/4",
      "12477173312736773742634062075/8"
    ],
    [
      "9472793618351204031",
      "-27563055418972565174507438250"
    ],
    [
      "2405362868251675131",
      "-556798281333894654401979450"
    ],
    [
      "-3328783012259680449",
      "3426199167221743157876813910"
    ],
    [
      "1298267613449879781",
      "-772272609062830126174901250"
    ],
    [
      "18105662516066890221",
      "-75837390034387450453872954570"
    ],
    [
      "-3758055332354304819",
      "456347839496730797081097450"
    ],
    [
      "3416550881574812781",
      "3911490465129675044910861750"
    ],
    [
      "-2959182554929992969",
      "-4324392427837480720681196250"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -86/139 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -129423262682594003679387T^8 + 364444960853480119379208T^7 + 145088936906457036995136T^6 - 946405361864597551050816T^5 + 1086632441482958356509720T^4 - 615454597853371985855184T^3 - 2089672621773109442565264T^2 + 1503858169634937349756032T - 268043453574349038086592,\nA6 = 22378678518203765279639595291703734T^12 - 97642937907003790975195419097186584T^11 - 57701568157490976356217548246274864T^10 + 692728062356311676289756774010506240T^9 - 165059119295086271477298303488050440T^8 - 2065127205357525454766777049159397680T^7 + 866901377553305534044230525750471600T^6 + 2900595200522009433908965902519647040T^5 - 1511852767062133534934112666639840240T^4 - 1121738997234616988726901721424515200T^3 + 1300199883149489416130125996732379520T^2 - 448873241175573293059242892011302400T + 53141649442568035635166156713288960.\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": "2026-10-18 01:44:17",
  "updated_at": "2026-10-18 01:44:17"
}