{
  "id": 4263,
  "curve_key": "16223554922459365157333968487998098225:-66767984317017065802372503359936235009131324030936509225",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-337990727551236774111124343499960380",
    "77277759626177159577984375591439095158720118318203647"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 257.0816374212798,
  "faltings_height": 19.322159585500675,
  "conductor": "77519333444665700271122771572822177358597129155530657165098398935235427803771301026650",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "109",
    "197",
    "848123011",
    "206803331064923",
    "716684121495967",
    "25601293634714065871",
    "32374867301916089857"
  ],
  "discriminant": "-108717297562017607394043209883866872004269333051384218482529289499686823652017744244499301325689310904320000",
  "regulator": "1777583406172718730373497.0779813197637155148641451437876384172228427491977002449397897",
  "points": [
    [
      "17478062179079125",
      "267162265139180935401961733"
    ],
    [
      "1018212826255971109",
      "-888127754207422011244053835"
    ],
    [
      "632875145679948949",
      "-341844865762129013718761755"
    ],
    [
      "1107545878836766069",
      "1030299662181403586864681285"
    ],
    [
      "318602999334585589",
      "-43972858795990064222646715"
    ],
    [
      "-351487090999232411",
      "390708722877737486691945125"
    ],
    [
      "-25875995514392518939/49",
      "112981026363718723363831021555/343"
    ],
    [
      "593930493853461685",
      "-293335609608744108975749179"
    ],
    [
      "1681185062906077429",
      "2064152619828313140331767365"
    ],
    [
      "607483661948006005",
      "-310060475259445460683200187"
    ],
    [
      "5776559597602186093",
      "13815961648839001622644463285"
    ],
    [
      "143871472179837790117/289",
      "884250298267314769009128273925/4913"
    ],
    [
      "2187366667685300725",
      "3131067464460896687902859333"
    ],
    [
      "-300644818931488331",
      "389510520058860602388027845"
    ],
    [
      "1171030211245984405",
      "-1134604734158640946328010619"
    ],
    [
      "-20725545538692936899/169",
      "751114754893092927436287454505/2197"
    ],
    [
      "-235642587232727051",
      "379259992885930589254900805"
    ],
    [
      "4246658149926240941/25",
      "-19671495922607921731875537679/125"
    ],
    [
      "337687908761050625",
      "-40620004334562934110761359"
    ],
    [
      "765010284783190069",
      "516165243379232361679760645"
    ],
    [
      "-140125422682858451",
      "-349123862942048283920705995"
    ],
    [
      "-463948842080620427",
      "366365747745135501344183621"
    ],
    [
      "3786612438678977069",
      "-7286393451068601640443985355"
    ],
    [
      "58761314173122251965/169",
      "93046984557580181142783943721/2197"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 1154/167 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4765105671341170713012T^8 + 114715794415427693698302T^7 - 1289703173484205490556069T^6 + 1970946774680673720492576T^5 - 1710136570699445082168780T^4 - 705937567588433468644896T^3 + 1908320361802866590386896T^2 + 127404060867858778875648T - 648856125950076308077632,\nA6 = 96897205978949562584426677136484T^12 - 5182597562294583468083790262057896T^11 + 84877162983356922665937799396845291T^10 - 478870362976518748392317900380853010T^9 + 1861233683275843787028761356431736485T^8 - 1364843279709253439363789384039551872T^7 - 1311792976812619745745993240617168352T^6 + 735145326496711370457296224143481152T^5 + 1094740667609718961081479717092760480T^4 + 53782848467549070290540339428638720T^3 - 759905051149062814344760081603028736T^2 - 65476590517227188924250720852312576T + 200491211946380337902432377627289856.\nIt is a 2-neighbour of the fibration given 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": "2026-10-15 21:44:36",
  "updated_at": "2026-10-15 21:44:36"
}