{
  "id": 4577,
  "curve_key": "1572418821410017176095676255515910601:-1995275883928265867777706591109040316900419268388905349",
  "ainvs": [
    "1",
    "0",
    "1",
    "-32758725446042024501993255323248138",
    "2309347087879937344235044396983813139764936209623888"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 250.06075470028554,
  "faltings_height": 18.71059406186483,
  "conductor": "325550369236788627718104773220234002353514063832382841479696492039232588130487188906570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "30653683",
    "751048873430637389460141677999796623",
    "225204387997853269648945329203998914787"
  ],
  "discriminant": "-54003948709689594975718186584382938746412566399296563590564349762911200920114290235267682822326194062500",
  "regulator": "4556079942979910750567422.5091548078411392847674409710827579623597543492307453628257849",
  "points": [
    [
      "106902393207420104",
      "5390222208494664227967360"
    ],
    [
      "207787663084580054",
      "-66886983692513303009904315"
    ],
    [
      "167257377211172927",
      "-38848922500191713210270043"
    ],
    [
      "1414858645124344336/9",
      "872666701801116624774315920/27"
    ],
    [
      "141061345978707539",
      "22253957650320747663087765"
    ],
    [
      "-61478336537351713",
      "-63960428233184311341075483"
    ],
    [
      "118278696549630379",
      "-9454574148876542915193115"
    ],
    [
      "-134798396431697131",
      "65389616747909525165235375"
    ],
    [
      "88675926764048549",
      "-10086268148367172700657805"
    ],
    [
      "780602045616884204",
      "672599078574973479933267960"
    ],
    [
      "4008389305591631429",
      "-8017139856501324923204941065"
    ],
    [
      "3000273417723239",
      "47022217748289536153618115"
    ],
    [
      "914489542495616204",
      "-858563522867030746618140165"
    ],
    [
      "101151723352328579",
      "5540462248150364823907335"
    ],
    [
      "105004865061047882",
      "-5225654288703944419828788"
    ],
    [
      "72117771069766079",
      "17942781210470884752626085"
    ],
    [
      "156518106947225954",
      "-31880732717786532204392415"
    ],
    [
      "407913095045419829",
      "-238370626762541571262969665"
    ],
    [
      "10572204093247454",
      "44319260229210976673225460"
    ],
    [
      "41435703794900991821/1849",
      "3166819862605017967842981171345/79507"
    ],
    [
      "188604807141536204",
      "-53290725661684957153020165"
    ],
    [
      "256590543801661264286/2809",
      "1324662107761421132908625796420/148877"
    ],
    [
      "17806079592247214982791/139129",
      "-757554502936941201412627837836255/51895117"
    ],
    [
      "91120348857449954",
      "-8995853513145868955793540"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 682/123 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -485042948797679528112T^8 + 12463578805199058894528T^7 - 230629938307243679610144T^6 - 1586012147509225586376096T^5 - 3868907398105357015696080T^4 - 6794745991541079206248224T^3 - 4791118686138149116505904T^2 + 6061871481875161826582772T - 1374235222299991775805627,\nA6 = 3820001086939854414872700973440T^12 - 155249980524531925200471635032320T^11 + 5279785372691676756614905714258560T^10 + 22439305421110286908829252745667200T^9 + 198311921848923368813090766393603840T^8 + 1955108933617356512048828761030033920T^7 + 6903605561322701279549833535328289920T^6 + 8139034537986456490540355512081445520T^5 - 1317692978359257302156310289643874060T^4 - 2476393922218195353910049397638432280T^3 + 5841882186136964852470754649206854356T^2 - 3899452237007593054578752344925650716T + 735364979113660346489805816953176854.\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": "2026-10-18 07:02:56",
  "updated_at": "2026-10-18 07:02:56"
}