{
  "id": 5976,
  "curve_key": "370065604148164158757827136:-4070330090685324087735502128183023391616",
  "ainvs": [
    "0",
    "1",
    "0",
    "-7709700086420086640788065",
    "4711030197549888534850246693553792163"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 183.52716759085988,
  "faltings_height": 13.338490537664324,
  "conductor": "55019607225895010678347358135946865524094880965978440",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "29",
    "31",
    "891481",
    "184684547713",
    "540741710471609589778681"
  ],
  "discriminant": "19740949857713368000750964507622345245515185501856512745350819802783380000000",
  "regulator": "503579714909526.30352612026773958285475855532126901804009847263657161925087",
  "points": [
    [
      "645148449171",
      "-75170383577084250"
    ],
    [
      "-2230625769354",
      "3287792663640573075"
    ],
    [
      "635552253471",
      "-260440852058054850"
    ],
    [
      "-1906820497629",
      "3532550479035546150"
    ],
    [
      "-400002430329",
      "-2780454603596465250"
    ],
    [
      "-2726379832509",
      "-2337738004829404710"
    ],
    [
      "397781631921",
      "1306596415633325250"
    ],
    [
      "606965267121",
      "505094227334515650"
    ],
    [
      "-3042396001629",
      "-77755245549978150"
    ],
    [
      "-1002198479329",
      "3380986535272914750"
    ],
    [
      "156564999531",
      "-1872911856494740230"
    ],
    [
      "2469613148046",
      "-856269332782943625"
    ],
    [
      "3485050794171",
      "4491135008040224250"
    ],
    [
      "6274245891321",
      "14259433831164562950"
    ],
    [
      "3954142519371",
      "6004144957638022650"
    ],
    [
      "-2401886996829",
      "-3061409093081907750"
    ],
    [
      "6695117481951",
      "15912247883624098110"
    ],
    [
      "-231610611279",
      "-2546419869001977150"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 113/69 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 14:24:24",
  "updated_at": "2026-10-27 14:24:24"
}