{
  "id": 4278,
  "curve_key": "2498637894275197394109915301866782016:-3960304975221405412135221039647457354845574920827670400",
  "ainvs": [
    "0",
    "0",
    "0",
    "-52054956130733279043956568788891292",
    "4583686313913663671452802129221594160700896899106100"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 251.43183211584847,
  "faltings_height": 18.763643508654038,
  "conductor": "80434146883505932726005348229594318875747348526136885446814145870458512275918533423530344",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "29",
    "37",
    "43",
    "745515769574693139059",
    "95061091737541505740475025201417024601534871192611368373"
  ],
  "discriminant": "-48924228379966546147736842866492934609598432604952731444588226184276407272649297064087580533366310298368",
  "regulator": "27965673808001077022803098.575100919616114389141500451445836157384698360718022921866668",
  "points": [
    [
      "108938266123823250",
      "-14343622810030489487314110"
    ],
    [
      "239079416445688086",
      "-76183661910242907782707638"
    ],
    [
      "116812366477241274",
      "9845989353724151003479554"
    ],
    [
      "129153229687557457",
      "-3868899608219416024496093"
    ],
    [
      "377496619863645396",
      "-196793751536174273099328402"
    ],
    [
      "-79855254736513868",
      "90726634346464274664383218"
    ],
    [
      "135072178896437050",
      "-4102859793121165066933250"
    ],
    [
      "106940953224495924",
      "-15488567545227907828842354"
    ],
    [
      "1263209450861613666",
      "1398044461224726642370304382"
    ],
    [
      "-124849674725890964",
      "-95585792255931469340071162"
    ],
    [
      "699730032540917097/4",
      "-230583101294659922856362667/8"
    ],
    [
      "167823911302044972",
      "23965763358342267645847482"
    ],
    [
      "-89466387771627566",
      "92329547022009184889655874"
    ],
    [
      "122164792636883308",
      "-6900699754250948600199674"
    ],
    [
      "-14113234336335900",
      "-72907742979659594054103330"
    ],
    [
      "1244354954459611218",
      "-1366232781194934157214865474"
    ],
    [
      "133560558715849137",
      "-3702298054389063143877357"
    ],
    [
      "-71312406887700942",
      "89068480271021843995962174"
    ],
    [
      "50217070474741382556/361",
      "-40167104733230053776221529582/6859"
    ],
    [
      "90210657457202096313",
      "-856811692206921972559493918001"
    ],
    [
      "324217663745304366",
      "147605448815660059062271818"
    ],
    [
      "222699139789077681",
      "-63528225680441404229953683"
    ],
    [
      "548767240503149609500/3481",
      "-3529293816530694055381480132190/205379"
    ],
    [
      "107238552095394372",
      "15318061843463908746774018"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 32/21 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -2350796244229826784432T^8 + 40408811499609701188800T^7 - 807647185297995630241792T^6 + 1124780763822387162339456T^5 - 1304766910580579021664360T^4 + 1443539650170624433343496T^3 + 1704268062115609657765788T^2 - 1468913167837302046081776T - 1000351384601036369237532,\nA6 = 39869593619137462773895754588544T^12 - 1348966735043080317092632272134400T^11 + 31027342372605406058463256507914496T^10 - 139468061144328757444897112746057728T^9 + 1081825061951776499965823580935603424T^8 - 1898481303093606040657233497704979232T^7 - 570283484013752985306584054565000912T^6 + 2509799809819326794944663142993968224T^5 + 574280708473637397501657996019459428T^4 - 2029433790678638479785535621658530032T^3 - 641250037642162230715032671759921448T^2 + 863840080098002956108405878211611888T + 384816973441734885044295380206073844.\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": "2026-10-16 13:48:47",
  "updated_at": "2026-10-16 13:48:47"
}