{
  "id": 6011,
  "curve_key": "122914789250142302824297985983576893376:-1379907570915185155415522884481846830961514090173176714624",
  "ainvs": [
    "0",
    "1",
    "0",
    "-2560724776044631308839541374657851945",
    "1597115244114797632729206190950223395851534923925596475"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 263.13873363997783,
  "faltings_height": 19.80284328945872,
  "conductor": "38394771744510785556176953859518468466663700500649746238666433145553214754846053363273466449179240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "1789",
    "117787",
    "5567363393160807858848091741206387951",
    "14354232369553341141842215891678113905167243259281"
  ],
  "discriminant": "-27281646950124129094890538479690162735339232372049831283285737670101653729308818747410150208302938811212000000",
  "regulator": "1502452129112257142854331917.371061474022946794019980233497818531687320668918314828762403",
  "points": [
    [
      "773778971875165085",
      "281012382545415061504779450"
    ],
    [
      "930652906644693335",
      "141497613626744400106981050"
    ],
    [
      "238498688545612565",
      "999975967777574757182270670"
    ],
    [
      "10553432833411045175",
      "33911070097424748870793629690"
    ],
    [
      "727441974511520735",
      "-345366985993446407657167350"
    ],
    [
      "53777727124925285",
      "-1208122846988744295975045150"
    ],
    [
      "41888637679314683",
      "1220624214083284142371366746"
    ],
    [
      "25203704670584821007/49",
      "221244516515392271188696015398/343"
    ],
    [
      "1051990028389525070",
      "259764923952519387995614635"
    ],
    [
      "528980111368356575",
      "624949565615528357765785590"
    ],
    [
      "109661839787444645",
      "1147876394245623784899965790"
    ],
    [
      "1019816306030033579",
      "-215130471758770908797748090"
    ],
    [
      "8744451748223562485/4",
      "-20312300374780914972109247535/8"
    ],
    [
      "-1830283224454696435",
      "-390683929304411430011827830"
    ],
    [
      "-223718227172934715",
      "-1469285196501256051683652350"
    ],
    [
      "-1436309438997028165",
      "1520534071744476350817087450"
    ],
    [
      "1818678803396060135",
      "1719135802126332746079428250"
    ],
    [
      "881449405972932035",
      "157514191310953622901940650"
    ],
    [
      "918258594804210035",
      "141358756035330526053511350"
    ],
    [
      "-1769066325227454865",
      "768599319870019138714598250"
    ],
    [
      "-318980724144401210",
      "-1543204851193604198882885055"
    ],
    [
      "76314646307313812935/81",
      "105201767870563601676934974250/729"
    ],
    [
      "832485000358054055",
      "-205641483928989748013926170"
    ],
    [
      "5671115901814540973",
      "13017943673135271492584086506"
    ],
    [
      "980952706243875755",
      "170601734139081634041642630"
    ]
  ],
  "submitter": "apkorte",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-28 02:26:33"
    }
  ],
  "commentary": "Specialization at T = -71/67 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -19381964681583531802332T^8 - 28905723289750482456822T^7 + 237762949204059961327281T^6 + 531898331411046911194404T^5 - 2081641537694219583469905T^4 + 2900998586783373204925386T^3 - 3510952046475025537069569T^2 - 2402026805831481679416408T - 336697228013419606811427,\nA6 = 1037857170981138962547584146233744T^12 + 2390096821086188960269294192921236T^11 - 17622524818710876412253124148231989T^10 - 68498401439427972797592193690386720T^9 + 142403571107393724072842085683710290T^8 + 537652195534688333016592840720348080T^7 + 242869176165494440760869297647114570T^6 - 5350043176257097379858948426236938120T^5 + 4432615889801018420373294120358506840T^4 + 3400474115253102291019214783235467100T^3 + 524125620210135846436694485054404435T^2 + 22638281992604199603670162474986120T + 4060904829303617481967199289389790.\nIt is a 2-neighbour of the fibration given in curve#4205 (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": "2026-10-28 02:18:24",
  "updated_at": "2026-10-28 02:26:33"
}