{
  "id": 5160,
  "curve_key": "114016990170780750551693358381662828881:-1217440823984210365497739268285850872622944955544802640985",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2375353961891265636493611632951308935",
    "1409075027759502737646659471099166373605792729134616201"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 262.8882324649833,
  "faltings_height": 19.54680668553622,
  "conductor": "70406956101573874140909238243890165565935985526040058829451404712463857460420580090848878",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17",
    "29",
    "31",
    "101",
    "1217",
    "374056178400297913150562417197",
    "1284587135853784193084942879863116960492221369803"
  ],
  "discriminant": "25666437320706702824811827158129450688897621471866484725947693239325375691710673274553454137482130568937472",
  "regulator": "8149153888758334152716316.7936302695067032452537956428860279172631484132062178832655461",
  "points": [
    [
      "893291760926288760",
      "-3329079650760372970366131"
    ],
    [
      "937167829672612590",
      "77902441859785068857891229"
    ],
    [
      "-825104908043225514",
      "1675488400463382347854254693"
    ],
    [
      "1062930126458559798",
      "291821757438510433884351909"
    ],
    [
      "771221475893282268",
      "189367702833152183942317269"
    ],
    [
      "15340060567984746630",
      "59789255409384487472555213061"
    ],
    [
      "881203890951813686",
      "-13288403289300791037129307"
    ],
    [
      "4355906110942931022",
      "-8585503002031073872544230731"
    ],
    [
      "932521919786250258",
      "-70169630473315442210999811"
    ],
    [
      "44474949543320436",
      "-1141717676397233783334708057"
    ],
    [
      "22081279477756912494/25",
      "1211397810347507862410634393/125"
    ],
    [
      "5898936215672390124",
      "13880379766651891672499446965"
    ],
    [
      "868915188353857926",
      "-33714699969156138989742219"
    ],
    [
      "1489771344091707721110/1681",
      "249615690790022979627479717949/68921"
    ],
    [
      "958947651312080466",
      "-114300392307364978656790659"
    ],
    [
      "43938010496030230134/49",
      "-3519379366581476705538986637/343"
    ],
    [
      "698956218981419126070/2209",
      "-86189389063905396622328233515093/103823"
    ],
    [
      "4076753134300730166",
      "7712369182884180511917606693"
    ],
    [
      "137609029866519624",
      "1041542448318052263580184715"
    ],
    [
      "876387347401339104438/961",
      "1072963422613776533141109437499/29791"
    ],
    [
      "588714946904945910",
      "-463366578766262718923234331"
    ],
    [
      "1241175729301001166",
      "610652019607407146863776693"
    ],
    [
      "45758697342939631077366/57121",
      "-1945158841376213023445447339349141/13651919"
    ],
    [
      "1122264835184879526",
      "-395938227617432220383065707"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1172/133 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -55167841848013120672432T^8 - 332957956141194498177568T^7 + 30491322260931582308864T^6 + 1529425586966988026755040T^5 - 1952037697734560475124240T^4 + 2598926506840431770721968T^3 - 1867830095998069273733704T^2 - 277424385594374102335720T - 14777266661889408077275,\nA6 = 4598281008482828350515082915932544T^12 + 42978899384640031706121578829901184T^11 + 92492192628018200121094722387755072T^10 - 190123782916092378560803318012553920T^9 - 804112508567836069639299650095483056T^8 + 453677299928650241856349297890606048T^7 + 3341413915638233675031424423024721088T^6 - 4626422467332761770277917962033627744T^5 + 1280672988092416347275859838092852864T^4 + 274908311165313855430793313344325200T^3 + 204841690501474358540727164780007400T^2 + 26424146202979804837762201204291000T + 968816204643834101037115185253750.\nIt is a 2-neighbour of the fibration given in curve#4191 (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": "2026-10-21 05:42:25",
  "updated_at": "2026-10-21 05:42:25"
}