{
  "id": 5977,
  "curve_key": "78415096357276105507000256221125133201:-694557742197454145799669531567694525073945209693693039801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1633647840776585531395838671273440275",
    "803886275691497853798665378509005054182227807131950625"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 261.76574064505945,
  "faltings_height": 19.53905440762625,
  "conductor": "767184420646850251170860010157875054011394223246364552948651118273090703689670790970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "31",
    "103552570267",
    "1735950052382287979273",
    "153545253088410405622926766477427549138230337"
  ],
  "discriminant": "-139888682619763220612450894292989216393432516999733029204363337268870503246745744979581765959004569600000000",
  "regulator": "760251331933429139419822.69037519637391911437433857392585813934697752734526278626219250",
  "points": [
    [
      "743599313353793050",
      "16511264290104476181584725"
    ],
    [
      "8495517444887661550",
      "-24496512429776026475846032775"
    ],
    [
      "742481158198209550",
      "-15724611343066478897176775"
    ],
    [
      "740005009581002956",
      "14523064768616481660998377"
    ],
    [
      "284940208240805050",
      "-601272715345822752124057775"
    ],
    [
      "739408348326150670",
      "14360902602360304600701625"
    ],
    [
      "532537664207966350",
      "291432694505461940809927225"
    ],
    [
      "3288230417267841550",
      "5566500985043723349042967225"
    ],
    [
      "675413466361589590",
      "-92794950765328870434220415"
    ],
    [
      "749931443249323840",
      "22841053776416534775014575"
    ],
    [
      "5097336572158161550",
      "11176757784634231022412871225"
    ],
    [
      "765407926610984590",
      "-43508190281342120287519175"
    ],
    [
      "633133374497097550",
      "152858762551463917681567225"
    ],
    [
      "1991042870531546050",
      "2333284914763901743414961725"
    ],
    [
      "748934726573265550",
      "-21692855022976005305272775"
    ],
    [
      "5385057956307164770",
      "12172390129992312429684007105"
    ],
    [
      "1120730982991665550",
      "-616998506385120498660472775"
    ],
    [
      "719320917903633550",
      "31017714461906299720999225"
    ],
    [
      "19076984175307750",
      "879049568784570792518062225"
    ],
    [
      "695984668016678350",
      "-63432491148577287592072775"
    ],
    [
      "733979388463665550",
      "15363063200625585683527225"
    ],
    [
      "3251256515738684575/4",
      "-913316429448887700886759075/8"
    ],
    [
      "743076512363133700",
      "-16126733074268213484220925"
    ],
    [
      "-1064307285561422450",
      "1156285215768913546906567225"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -488/111 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -36741768965072427329307T^8 - 175652477872961149894896T^7 + 69292619378708331563604T^6 + 676777688422838786893536T^5 - 656364464021699831415330T^4 + 2063898400836725040248640T^3 - 1358206219455103158319372T^2 - 1679620299616449035353360T - 380387730244665052932907,\nA6 = 2972887747061499967014816310768950T^12 + 24971701851338630896585499476986576T^11 + 40958623108017859037060407448604996T^10 - 185504583684287485388498717737301760T^9 - 545461524648606440857833405079456086T^8 + 682919486625522225231856567512795600T^7 + 2337615182727970756165249196632581528T^6 - 2526741785379638456321704985966591088T^5 - 1756453725043689246538106067241758246T^4 + 628926877625456418301614685250524320T^3 + 1296733620825853845986136477111316036T^2 + 591132703001133261198186526777781680T + 89026717350891792884482981951773094.\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": "2026-10-27 14:31:46",
  "updated_at": "2026-10-27 14:31:46"
}