{
  "id": 4555,
  "curve_key": "5204431846619046826955238337405214046481:-330492228375281077668718238816887723734277766207765316667129",
  "ainvs": [
    "1",
    "0",
    "0",
    "-108425663471230142228234132029275292635",
    "382514153212130876922351378526573094321579755441733212497"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 274.3509875027049,
  "faltings_height": 20.84547558498979,
  "conductor": "6211004779178492809579744073240143386701604826069736785648084946384192134182454991888528130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "73",
    "2417",
    "1311198157",
    "326962519007931381802849821884118161643340185389096681227585234200358259"
  ],
  "discriminant": "18369620875029340952186658212655856173124724701381002479037718372866607001214779196654426879538805176468531200000000",
  "regulator": "34076960793385080500624961.23655607136906692914958441742911338441009300288398063079194916",
  "points": [
    [
      "44071919552094710334",
      "-284967329597884765789206087567"
    ],
    [
      "2521653136624377534",
      "11186454384769056643664238033"
    ],
    [
      "55215996290680872894",
      "403408673047076679040532250993"
    ],
    [
      "2427527429885599134",
      "-11559110336677235165035013967"
    ],
    [
      "29974829595388842174",
      "155127593526369240902094264273"
    ],
    [
      "8006549126167913694",
      "-5259012647342399528686337487"
    ],
    [
      "109007192752707183409896/26569",
      "11233143432023341050077540296504101/4330747"
    ],
    [
      "3844567260202343334",
      "4742339361932571740576035233"
    ],
    [
      "-9464869492072632066",
      "-23682279501001741386897565167"
    ],
    [
      "-11666228457334988766",
      "7723255776483604214379540633"
    ],
    [
      "16411086036194275484",
      "54982055340708119104965094883"
    ],
    [
      "50228176978180415474286/25",
      "-11256809101220000540174744887767699/125"
    ],
    [
      "1578536453781283614",
      "-14672888341426990802393028687"
    ],
    [
      "3431901726699489024",
      "-7129424706511190814613930377"
    ],
    [
      "855101830515805415454",
      "-25003147624036850010335938400847"
    ],
    [
      "3987118299633816342",
      "-3686715849378627969921965655"
    ],
    [
      "16221571959368836734",
      "53779309322173297807017819633"
    ],
    [
      "-101318157631300192131/16",
      "1827291640006154194697091496137/64"
    ],
    [
      "13766014115793426174",
      "38712115711615382769323585553"
    ],
    [
      "-11170767109254393342306/961",
      "253167115364885269917667918374063/29791"
    ],
    [
      "73741059151715990814",
      "-627193812548198302154999057487"
    ],
    [
      "9115372317315751734",
      "-12311387479389856545899885367"
    ],
    [
      "29249034028220242568256/2209",
      "3697400417286742449898153276631559/103823"
    ],
    [
      "-1659701904803791266",
      "-23619834910867021166785244367"
    ],
    [
      "11265205289130010734",
      "24304032280352705666264517633"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -173/66 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -129423262682594003679387T^8 + 364444960853480119379208T^7 + 145088936906457036995136T^6 - 946405361864597551050816T^5 + 1086632441482958356509720T^4 - 615454597853371985855184T^3 - 2089672621773109442565264T^2 + 1503858169634937349756032T - 268043453574349038086592,\nA6 = 22378678518203765279639595291703734T^12 - 97642937907003790975195419097186584T^11 - 57701568157490976356217548246274864T^10 + 692728062356311676289756774010506240T^9 - 165059119295086271477298303488050440T^8 - 2065127205357525454766777049159397680T^7 + 866901377553305534044230525750471600T^6 + 2900595200522009433908965902519647040T^5 - 1511852767062133534934112666639840240T^4 - 1121738997234616988726901721424515200T^3 + 1300199883149489416130125996732379520T^2 - 448873241175573293059242892011302400T + 53141649442568035635166156713288960.\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 01:39:43",
  "updated_at": "2026-10-18 01:39:43"
}