{
  "id": 4597,
  "curve_key": "22519749254741076843883625114811427009:-79863208663974130943680143863829358783770806297368089377",
  "ainvs": [
    "1",
    "1",
    "1",
    "-469161442807105767580908856558571396",
    "92434269287007095804145861635730650989170854092919429"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 258.0223680499758,
  "faltings_height": 19.52201191293812,
  "conductor": "90768017431890829871720181326988326138150445714817351174485656583597333916013927166435420090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "97",
    "199",
    "46457",
    "16941111922860221119",
    "112454062659905351733878800067433744181683847668968935740457"
  ],
  "discriminant": "2918121190663854725137527318737780000313483980914697560908953701977099429994158324256020168477002138087731200",
  "regulator": "554782003118680460972586497.1515206298403419871367707513958383538052776830983358032387189",
  "points": [
    [
      "723548309199517371",
      "362997067423143889126928983"
    ],
    [
      "568405463460022653",
      "96971598062688468392176657"
    ],
    [
      "14550727989162127229/25",
      "-16073856801762031302825392827/125"
    ],
    [
      "19581806917244632989/25",
      "56665516434998667970310535077/125"
    ],
    [
      "1413900526547227101",
      "-1501877486978420962974101807"
    ],
    [
      "198005550919029419",
      "85444392385297856563679975"
    ],
    [
      "970837330451231021",
      "-742962583741882220175619055"
    ],
    [
      "548247988709514789",
      "2749728956960097116901265"
    ],
    [
      "-163767047928267907",
      "406048371002761176018424849"
    ],
    [
      "203882427224494269",
      "-72494753703438808518337775"
    ],
    [
      "579222797309129213",
      "-122531480351660387188809743"
    ],
    [
      "-151509936783396171",
      "-400048671579870400016164295"
    ],
    [
      "17531741523249803589/16",
      "-60510706762148192633349745265/64"
    ],
    [
      "-758331324501112947",
      "-110105515181933255019439343"
    ],
    [
      "1276722072287975729",
      "-1254801600234320017691068735"
    ],
    [
      "192640181601374461",
      "-95936682516653240935893775"
    ],
    [
      "14568471002587364911/9",
      "-51046741087510917351674501015/27"
    ],
    [
      "-753746802413338021",
      "-133543394284417043000614985"
    ],
    [
      "-392196399182366979",
      "-464877215819358254026615055"
    ],
    [
      "160742945283591793461/1849",
      "18183429229091142287929379370115/79507"
    ],
    [
      "1934072226903783376389/3481",
      "11763841097931723450460909308275/205379"
    ],
    [
      "598644311153285697",
      "-161593942939671575747576579"
    ],
    [
      "671242672796623629",
      "282759087461665193689028065"
    ],
    [
      "131632813586869577567693/214369",
      "-18799529238662469867377002941642913/99252847"
    ],
    [
      "2353162331571404631/4",
      "-1132220008569243924936375205/8"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -197/83 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -131683424850520935576768T^8 - 403203691800547711440768T^7 + 228773565844968202575408T^6 + 1001632750223305381512624T^5 - 240565012803414935795880T^4 + 1113998583596965801461504T^3 - 955469793798674292115872T^2 - 990503756503270017161688T - 226533255431841379251243,\nA6 = 19076424418751512058704915856577792T^12 + 97086137010965231517170399109938688T^11 + 56104518594343130212702088417622912T^10 - 478767125533383624912178730778518400T^9 - 714366843201118889959457857278267504T^8 + 1042906926398973532541608382597231424T^7 + 1920199847343299876864028118527850608T^6 - 1651848617855242258127597768465390256T^5 - 1294346250171073842969926939033547144T^4 + 242314299085392499926732997139536320T^3 + 623077991032626826626842144461126512T^2 + 269831263748284750614515352678364488T + 41099644923330823113323890449407142.\nIt is a 2-neighbour of another fibration built here: 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 20:16:51",
  "updated_at": "2026-10-18 20:16:51"
}