{
  "id": 4237,
  "curve_key": "441075230143913957405754765179337026641:-9268384262390359399743426387672470193874479665253215081689",
  "ainvs": [
    "1",
    "0",
    "0",
    "-9189067294664874112619890941236188055",
    "10727296599988841897085432340806249140932693885977094377"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 266.94791873514004,
  "faltings_height": 19.997124107425467,
  "conductor": "62659003164479686239328068266541122033367068516956338027806434655324043652257974884230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "79",
    "3498445730203303206559439929",
    "260332218151053659462503699988537659980818327556319"
  ],
  "discriminant": "-53776531496985407486180632129337930670769080170196077225835567106569557337859667173261047054201371172864000000",
  "regulator": "1410984072986437583877762.1189554013978907003531185512350672277860087120021144952549299",
  "points": [
    [
      "590004994880431594",
      "-2347570066137968070712947047"
    ],
    [
      "221715824581223254",
      "-2949717622778522433481908587"
    ],
    [
      "4019127130004479894",
      "-6222360192452655871886312747"
    ],
    [
      "-165414514065273247514/169",
      "-9521838682300797480254398404359/2197"
    ],
    [
      "4221539659301752342",
      "-6867970532370704250479515307"
    ],
    [
      "-935264079507713786",
      "-4301558786706113151917578427"
    ],
    [
      "-2947621543968607406",
      "3493259198283447915716669953"
    ],
    [
      "-107152262846726186",
      "3422089372621955622976913173"
    ],
    [
      "2180535375688755094",
      "1028628759615998185289602453"
    ],
    [
      "-1437969921314699882",
      "-4579031107805763187416522539"
    ],
    [
      "1375411824635693014",
      "830957686596752751086286613"
    ],
    [
      "1676833536930188464",
      "183389783049908438952776323"
    ],
    [
      "14995848968483305651/4",
      "-43057867663770874648012675201/8"
    ],
    [
      "6771462199853767894",
      "16093281258301385676838776853"
    ],
    [
      "-1203332191918229546",
      "-4476869665880211544671289067"
    ],
    [
      "-3203788854594406706",
      "-2698628632204478746530600347"
    ],
    [
      "2003085275381266774",
      "-598240466907045954298940267"
    ],
    [
      "1792345254931721044",
      "123398865438655023291754903"
    ],
    [
      "2210148244029665494",
      "-1101875182837009365168954347"
    ],
    [
      "1759681768750395814",
      "-79257083021118506292684827"
    ],
    [
      "1910839600114719094",
      "381479750264758270531510453"
    ],
    [
      "2646873734002597654",
      "2224597894463318389922216533"
    ],
    [
      "9078878610613200599974/7921",
      "-919369750523556388807391608246243/704969"
    ],
    [
      "1559189441704794454",
      "436235308750231437199462933"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -284/39 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -9879263860426790634432T^8 + 86542933653687887807616T^7 - 135085452380206943680656T^6 - 670355493830703722869488T^5 - 1051946747940271972123080T^4 - 3373640011473668508665088T^3 - 849884467368517694646336T^2 + 3646401529809912988876056T - 1342215706985392840165467,\nA6 = 376157002259901169222608370611456T^12 - 5012568105195271642968657466363392T^11 + 20939308987938975132973897671040896T^10 + 13327362718284003523861442478906240T^9 - 278883358041208378819482351125270640T^8 + 367979789534049131266298576914822080T^7 + 2889329182749276846125866347500564400T^6 + 1554211227618089538131391252658550640T^5 - 3013942383637349393404424222146644840T^4 + 631952356094086111413853506833246400T^3 + 2160468957381686900407596405190211280T^2 - 2226612923028643159215506958258590280T + 628996598302785742517854074617969910.\nIt is a 2-neighbour of another fibration built here (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": "2026-10-15 08:08:04",
  "updated_at": "2026-10-15 08:08:04"
}