{
  "id": 5857,
  "curve_key": "22598270138246876725755965264441461186425:-3091938774135782861888193179884710544862621641718149830552525",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-470797294546809931786582609675863774717",
    "3578632840434933868043848837392154502463568848852009729041"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 278.75607596268316,
  "faltings_height": 21.198129186313032,
  "conductor": "34323368201782394984208127638439954785918722081299558491309614362603772663830173776217449523450",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "31",
    "41",
    "53",
    "109",
    "199756568527978213006300391802901492439260471049243347550166556625558371368379241"
  ],
  "discriminant": "1146088071359751368030739931422069120842853922437098210372521071947903485016347662072769386018681723258204178876942500",
  "regulator": "454354993618082092382647406.553508719083677861087849307569268353229909795760670757535337614",
  "points": [
    [
      "78352946984405527429/16",
      "-2386563282101935396942698543443/64"
    ],
    [
      "247995563604802454989/16",
      "144255388648508467040217401107/64"
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    [
      "-5598617043887373386",
      "77710750058910290398742487853"
    ],
    [
      "225921807525821339971/4",
      "3171500805073444925988969395009/8"
    ],
    [
      "5855886099467327614",
      "-31976617272311941075707357647"
    ],
    [
      "23194042516291530934",
      "71669318222025253263977696893"
    ],
    [
      "65715281271664477891/4",
      "-133441369428148572550912692271/8"
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      "27793962559312285662138026623"
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      "-24690001981579229756",
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    ],
    [
      "-190308526252199683304/9",
      "-1724439486378826130987996454949/27"
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      "2390571419506839084695/4",
      "116807254896549807214221375213683/8"
    ],
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      "702897260016237978589/16",
      "16649884065482710436259987864907/64"
    ],
    [
      "3541484741833691164",
      "-44223626167969891184740298867"
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      "-2370548688199125356",
      "68420460745831254518669033413"
    ],
    [
      "1421553580225475786665/9",
      "53113978163939210532228512566937/27"
    ],
    [
      "-532013573443111292399/64",
      "42584788498197767667485687875901/512"
    ],
    [
      "-16145883164490052511",
      "-83492562811965574414164527717"
    ],
    [
      "132240946444835671285/16",
      "-1016092436171423210353300784891/64"
    ],
    [
      "26669889491293041659",
      "99961793564006538923738241748"
    ],
    [
      "2504129792642553129319",
      "125305172427854216523073721357668"
    ],
    [
      "-10860310658656010954216/441",
      "-142736759292749995107226774236947/9261"
    ],
    [
      "-12108791201003368381",
      "86625595604295971326393792393"
    ],
    [
      "44074794974551443229",
      "261624705778800538244151134308"
    ],
    [
      "15868856895810388324",
      "10184464411664673871267720903"
    ],
    [
      "-12304134874879571891",
      "-86652420183065273617302510257"
    ],
    [
      "-3046971747248545241",
      "70603475112053044222089742948"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 261/88 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -52356648678628357469952T^8 - 235519746807875124250368T^7 - 24545191841476895540304T^6 + 811577658055960647489456T^5 + 1079198714145333325459320T^4 + 1254987224811203628397824T^3 - 2522642567144527246899024T^2 - 3309712733210337229896792T - 1026058563214366117251627,\nA6 = 4825422219471759579683602107703296T^12 + 34580942274254747650686461570052096T^11 + 31234725928512794727685620659061504T^10 - 273042568629290335756659313007525760T^9 - 455151540100143399461517346503626160T^8 + 1043526152788429910684337802802723904T^7 + 1849381307726983593819115896264667824T^6 - 2215248076398208412328290355259090224T^5 - 3463947301549821564345287894913712680T^4 + 637485311836301536434086156313792000T^3 + 3271887185791747167987145751440802304T^2 + 1998129610230740561490595569733249224T + 403271364874736900390724325685972646.\nIt is a 2-neighbour of the fibration given in curve#4647: 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": "2026-10-25 13:59:37",
  "updated_at": "2026-10-25 13:59:37"
}