{
  "id": 4216,
  "curve_key": "20016139831214309439704901997612657825:-91613018625800855988196551543031836413863787190793920625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-417002913150298113327185458283597038",
    "106033586372454694396032803004873116035076891428674692"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 257.7143368159912,
  "faltings_height": 19.377417588240924,
  "conductor": "41404912517380058053828849521248900062672758440465027805081569107175800922832702586050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "37",
    "47",
    "379",
    "11243",
    "59311506215167649",
    "83590483637079143",
    "441972143131711413135924077034107198791"
  ],
  "discriminant": "-216181568530517366146285615548514438091945952930159580565362987329311859357695094068512883186262749184000000",
  "regulator": "8351713420605395981457695.6609688787137089192372765318058739058321394487147395015492810",
  "points": [
    [
      "452909821515327932",
      "-100364551473740612072698366"
    ],
    [
      "26893074564522932",
      "307958675809150679854246634"
    ],
    [
      "309439289002661852",
      "-81401109775008669698336926"
    ],
    [
      "80294065915455932",
      "270311660496309622594309634"
    ],
    [
      "9937749701269299044/49",
      "59213789518767364987517544590/343"
    ],
    [
      "370615051910158232",
      "48908608682303413766437634"
    ],
    [
      "38101740400185602",
      "300333753578466124472544824"
    ],
    [
      "385154128915423952",
      "50580453738211205905700174"
    ],
    [
      "270313833212840732",
      "114296305974776688909049634"
    ],
    [
      "71343451738511991932",
      "602578245546381469636709485634"
    ],
    [
      "20548189539726374828/49",
      "24029729105315787318148425902/343"
    ],
    [
      "-93259647989766244",
      "-379620887616705241470199870"
    ],
    [
      "-9509914459154548",
      "331660049367939551387058674"
    ],
    [
      "-143902333740438148",
      "403808576323412947296843074"
    ],
    [
      "1443478023679801532",
      "-1584856913736835486160837566"
    ],
    [
      "99215169658399723868/169",
      "-553884995845824173465006910742/2197"
    ],
    [
      "17182537567242344357/16",
      "60605247067871861396494082261/64"
    ],
    [
      "-244228361978495272",
      "439670234877708379866953510"
    ],
    [
      "611613136962852782",
      "-282445813822635639472551316"
    ],
    [
      "4711228508374275452",
      "10134610496279983145363095874"
    ],
    [
      "429721730473914716",
      "-78683649615143594998602046"
    ],
    [
      "308687240288603822",
      "-82001461952607999156661786"
    ],
    [
      "89383157298000032",
      "263580467012109448980223934"
    ],
    [
      "448575820244498372",
      "96118201279735576347151514"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -281/849 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -123856789139706169159947T^8 - 444860715403915335809784T^7 + 386197275608827081416504T^6 + 1527252937315431153244272T^5 - 1375436505233375995520880T^4 + 1122976665942695182127232T^3 - 920913248897305236746496T^2 - 558254638916475632295264T - 66664274811511860464112,\nA6 = 16359416402689331569871278519529286T^12 + 84307064804680497817942655822018088T^11 + 43582982500411768342190410573462056T^10 - 406313301062273227318175674455353520T^9 - 696574825662812869066591591106450400T^8 + 831815699985675007793533243030026816T^7 + 2339654226324227927870456252492273088T^6 - 2418192605459673378876521710121559264T^5 - 588423094738870081007533655250779760T^4 + 462827873819015983743769059572260800T^3 + 312326563016748800922506015981603904T^2 + 77162055820545612135770412695494272T + 6735862148389763480692013144006784.\nIt is a 2-neighbour of another fibration built here (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 04:24:43",
  "updated_at": "2026-10-14 04:24:43"
}