{
  "id": 5961,
  "curve_key": "235157739834750551493985921:-3933530141584168702966273383278992572865",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4899119579890636489458040",
    "4552696923129416627727455159087675456"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 182.34071180863103,
  "faltings_height": 13.158598102455741,
  "conductor": "63044514070012459991780780537307987798970558879949106",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "31",
    "53",
    "61",
    "380411825191",
    "1711783233163844059855852137038987"
  ],
  "discriminant": "-1428607223377261901871995728217562082723857907876104087722646581062972735488",
  "regulator": "923259742420047.37081156069286761429596304363726309979614405523532690446710",
  "points": [
    [
      "7040059187576",
      "-17860156640330282944"
    ],
    [
      "3245650279664",
      "-4779368287328072824"
    ],
    [
      "949346147696",
      "870253819143328136"
    ],
    [
      "1279301339570",
      "-615603190149699676"
    ],
    [
      "-493167225472",
      "-2617028030543804536"
    ],
    [
      "75625995632",
      "2045147549592965384"
    ],
    [
      "2360410778045168/1681",
      "-45825698396594848924856/68921"
    ],
    [
      "-37990653274048/361",
      "-15439761581764182163864/6859"
    ],
    [
      "29207606864",
      "2099911955220423560"
    ],
    [
      "-721826504320",
      "-2777213259264502024"
    ],
    [
      "3184684520432",
      "4609803536087719304"
    ],
    [
      "1099077877424",
      "-704158539130293304"
    ],
    [
      "238274873895536/169",
      "1470617166337352945192/2197"
    ],
    [
      "1084956657170",
      "-717287499686596444"
    ],
    [
      "-2344864920592",
      "1774116509597777288"
    ],
    [
      "1462716587432",
      "-718480951615085296"
    ],
    [
      "18153432312080",
      "-76798628336586696856"
    ],
    [
      "1402008884060",
      "663261648307293836"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 3/4 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -78933294009407830037787T^8 + 664351884165635092112904T^7 - 2021985732877889552885376T^6 + 548914813539097302606528T^5 + 640067948619176548996920T^4 - 1474849384729522256976912T^3 + 590464289390067586470384T^2 + 586034868174794137776384T - 300031800937869261707712,\nA6 = 8561696935567950178044488886746934T^12 - 107576211314584682375352315962746392T^11 + 546348427718307812695067413402466064T^10 - 1166581522203545622660674205159843840T^9 + 773302754513408948238245171376141720T^8 + 1872425742961196136859874329988857104T^7 - 1253513330397887853768088296036034512T^6 - 1224384265855733627043677184733740096T^5 + 513489745068218712536403992172247440T^4 + 606394277930394193521826714846596480T^3 - 152435778857543725795710547166980224T^2 - 181401199060234447536055851013959168T + 63554942967600090043999344449500416.\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": "2026-10-26 23:42:27",
  "updated_at": "2026-10-26 23:42:27"
}