{
  "id": 4211,
  "curve_key": "892751287761584538895628191183441:-26658663996506943310954282617659141181381163148761",
  "ainvs": [
    "1",
    "0",
    "0",
    "-18598985161699677893658920649655",
    "30854935181142293948874248813984181525392218025"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 227.61558245628288,
  "faltings_height": 16.722621391212808,
  "conductor": "2868141892098437145536875583170573908255125303354625939834791533890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "37",
    "41",
    "52258860304031",
    "366299151170861039048009645391843396287221"
  ],
  "discriminant": "487702919854845525075037664475889107337308246810453073077767113830583096951162955246400000000",
  "regulator": "5233349011910443319.5582020074231339066766689861111105546394709674791849400894805",
  "points": [
    [
      "3708882781803110",
      "113543697828814231602245"
    ],
    [
      "2580418604525750",
      "6606086692954260310805"
    ],
    [
      "-1791031557593290",
      "241704457181550454730645"
    ],
    [
      "2564233800265202",
      "-4835538431497589517619"
    ],
    [
      "41171887479444710",
      "8310028097342846628392645"
    ],
    [
      "100437896280710",
      "-170258349134906634963355"
    ],
    [
      "2439625866036710",
      "687451548636429512645"
    ],
    [
      "2544379500316460",
      "2008280959713602098895"
    ],
    [
      "1598179942080710",
      "72197284484636658986645"
    ],
    [
      "2223914137480310",
      "-22167782621100835149355"
    ],
    [
      "2561508277159820",
      "4513107727767130370885"
    ],
    [
      "2437793730243860",
      "-1363688307831837498505"
    ],
    [
      "4297376855325542",
      "-174039278534865556701883"
    ],
    [
      "-4324252382147710",
      "174418348883410239046445"
    ],
    [
      "2987788782074210",
      "-44234979472666196862355"
    ],
    [
      "2247661343880710",
      "-20145937762156870563355"
    ],
    [
      "58806059233910",
      "-172514942913663230241355"
    ],
    [
      "2542182678077030",
      "1504287138212796256325"
    ],
    [
      "4702091637588710",
      "217629216973006288322645"
    ],
    [
      "29535087359617715/4",
      "4353118593758287304939035/8"
    ],
    [
      "2469789810501862265/1024",
      "169291733947357940065232035/32768"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -653/146 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -1383044527665321116400T^8 - 16049999528139513071520T^7 + 15805299603407933138816T^6 + 712593854642478382322880T^5 - 3813994880887522829708400T^4 + 10533902963478229407850960T^3 - 10115880489507421099979016T^2 - 8597064026478854771701800T - 1511313760202147775869947,\nA6 = 19606871590209659689292333520000T^12 + 323679316365878812163330339568000T^11 + 983969135059873668251937025883200T^10 - 6275524572874812809451065998804160T^9 - 65918284694373505756900522296861936T^8 - 337269555874810038655223788688478240T^7 + 5081060790854484290367532173908523840T^6 - 14611633213803604472414514215799717120T^5 + 11577647003766635578545334685110815264T^4 + 380100766090866777957899579121104880T^3 + 4610206606796227830325446909775634088T^2 + 8093183322260907342485075849728593400T + 2171157485142496238941816568266368214.\nIt is a 2-neighbour of the fibration given in curve#4191 (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": "2026-10-14 01:31:32",
  "updated_at": "2026-10-14 01:31:32"
}