{
  "id": 4281,
  "curve_key": "22179549930402837052220450479069809441:-101296114320485036603646148844885032909988129610946867761",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-462073956883392438587926051647287697",
    "117240873056116940628997828161687268107615922183751169"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 257.97670211344774,
  "faltings_height": 19.41340871403325,
  "conductor": "75658910303290538667272432081894152972706180017093521752285062478585089190",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "31",
    "83",
    "101",
    "30089",
    "2215341147311",
    "4517963993642910826508666609592000581408041"
  ],
  "discriminant": "376121082519779690832781742503478767650138384955117580720528315657208774428663148072598636627195494400000000",
  "regulator": "239900305773727880297.9155277137260633018666668109138020920498031534885463354105746",
  "points": [
    [
      "-326634504311987433",
      "-483033645852522294780794764"
    ],
    [
      "548326315307823127",
      "-169511980221807853756743564"
    ],
    [
      "-388141799797713523",
      "-487971262880544209610037414"
    ],
    [
      "853930899516323727",
      "587661748693615516345282836"
    ],
    [
      "-466184160923234623",
      "480975794387208579974651686"
    ],
    [
      "233798314596538563583/729",
      "888045404584667157716667501788/19683"
    ],
    [
      "596533477577075127",
      "232112112667331613230344436"
    ],
    [
      "-741078579030254313",
      "-229511461098930553927856524"
    ],
    [
      "211584881021702627",
      "-170133112902847944988983064"
    ],
    [
      "2065431428560809964807/36",
      "-93861139432197757077846264521299/216"
    ],
    [
      "-219804579407251673",
      "456275349736164970764845236"
    ],
    [
      "261113245321977227",
      "119958229234086467113874336"
    ],
    [
      "607435767609359127",
      "246355814855392331153720436"
    ],
    [
      "147875623014273047",
      "-228352851182529269155303564"
    ],
    [
      "220601477114306727",
      "-161376110788118240461791564"
    ],
    [
      "312056560696538327",
      "-58613239373175959271143564"
    ],
    [
      "335133208445711127",
      "4978567459413572981560436"
    ],
    [
      "-310166610712500873",
      "480335014985486453766860436"
    ],
    [
      "134535055217251127",
      "239814030686104102060488436"
    ],
    [
      "94387974547458107",
      "-272887447743686596542923344"
    ],
    [
      "-730311286878171273",
      "-255311246093495279241331564"
    ],
    [
      "971400488516237516623/3249",
      "-14121707921120878937474253731852/185193"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 400/29 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -8921224827903176421867T^8 + 94634723251967943349008T^7 - 153371039643193058472636T^6 - 641050270990816586343840T^5 - 1411956329363864664615090T^4 - 3616744002660872511746400T^3 - 276286449215617413614716T^2 + 3264390669786107213517648T - 1094619040863704280589707,\nA6 = 270621608798713355418362188083174T^12 - 4440334258578316878189533038482864T^11 + 26574225298655897363019125632965972T^10 - 44466546059753405576217220076774400T^9 - 266551804859294565919720379747154006T^8 + 857066304185931807663129817734860208T^7 + 2882807104710383577362230811059875192T^6 + 490875434163168933481957024140491568T^5 - 2474513386731796364719321202224339446T^4 + 1633690238596691275986648934120443840T^3 + 1554365531979876509922013707743895892T^2 - 1882445996339364406394564636163936624T + 453429930884494956186985826996791494.\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": "2026-10-16 15:24:20",
  "updated_at": "2026-10-16 15:24:20"
}