{
  "id": 4222,
  "curve_key": "14213231675796565028095446187577222401:-54517316132053873812526792032888800737014223168691787649",
  "ainvs": [
    "1",
    "0",
    "0",
    "-296108993245761771418655128907858800",
    "63098745523210502073156185786104112494063719776997632"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 256.6762268001534,
  "faltings_height": 19.27843884304181,
  "conductor": "2338316115837191674733629561727536281841554758951445057531174296600730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "29",
    "31",
    "37",
    "47",
    "53",
    "97",
    "13119857",
    "42534538278261919263861718677607149403105997"
  ],
  "discriminant": "-58355435365895417048106868394053496017787390947135560508459480149762425027833237290232922431669779456000000",
  "regulator": "4894717207613552166.9120291293895279491717325424063584941956092099141176210737894",
  "points": [
    [
      "417863685871341104",
      "-111034920099736374623063152"
    ],
    [
      "656654533550033504",
      "389619942862855830799983248"
    ],
    [
      "-629028544111057696",
      "21626008808152031951285648"
    ],
    [
      "259103251668985664",
      "61406094723086628920084528"
    ],
    [
      "-297291614797214251936/841",
      "-8574365489872302974974192167728/24389"
    ],
    [
      "-847283388019041464/9",
      "-8106335586195297837523180304/27"
    ],
    [
      "309363709606356254",
      "33185880452605700264412998"
    ],
    [
      "354276784437175904",
      "-51577180105724384728362352"
    ],
    [
      "369142766852505404",
      "63984387481251209902574948"
    ],
    [
      "426899139081554534",
      "120371913668410483425198428"
    ],
    [
      "306850692166313144",
      "-33611652528667191212376112"
    ],
    [
      "35759078633705376344",
      "213810726825527294443035568088"
    ],
    [
      "815355432752793782",
      "-603089226875631178529649682"
    ],
    [
      "13526901258483095654",
      "49710866542943621871645083198"
    ],
    [
      "249068053133579984",
      "-69270236207520892476438112"
    ],
    [
      "216398962856902064",
      "-95680237001335437604039792"
    ],
    [
      "-220504948380516496",
      "343031714209958664699663248"
    ],
    [
      "-365337128810599096",
      "350023375804614823970986448"
    ],
    [
      "367880475830642624",
      "62876995903343609450149808"
    ],
    [
      "-461109156560342896",
      "318740524771527507103272848"
    ],
    [
      "42982957154016929775584/3721",
      "-8901658654979885790514712213592112/226981"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -11/115 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -1294316468457527272747T^8 - 61482963914543295234088T^7 - 943435684374763790645824T^6 - 2688743270213054211837664T^5 - 3856670928366631764978280T^4 - 999902363213138391166096T^3 + 2961913384000561526356496T^2 + 1046903749166543421058688T - 943686476906321498328832,\nA6 = 32662063813788609918746258888614T^12 + 1796450107115792990741776388684984T^11 + 35062265377401817193324124680756816T^10 + 316874613294458685885325494699025760T^9 + 1878352364777031985219759926555560760T^8 + 3544464889310281997809284624918208080T^7 + 1303911666228891105042353858020750800T^6 - 1471880942788787576791593483327263040T^5 + 252670343673375657835921804367034960T^4 + 730639334234102885410704041977318400T^3 - 1097948334966447155670068911813786880T^2 - 383111400250142557306211553242163200T + 375132589068583102936074200430223360.\nIt is a 2-neighbour of the fibration given in curve#4187 (itself a 2-neighbour of the fibration 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": "2026-10-14 11:24:57",
  "updated_at": "2026-10-14 11:24:57"
}