{
  "id": 4205,
  "curve_key": "5372900915504809595273952195431375493285361:-27646280627436995623216827154640256685700067625610741028350785609",
  "ainvs": [
    "1",
    "0",
    "0",
    "-111935435739683533234874004071486989443445",
    "31998009985459485675010147920447916054753653584858326348507937"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 296.76470412271675,
  "faltings_height": 22.778770334058013,
  "conductor": "979409504419896215116182467439254200955571188757207790219066305425460761435416461348377034210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "29",
    "103",
    "137",
    "293",
    "41890943",
    "3466096787",
    "9396217511",
    "14868139758072059",
    "53187089596512271",
    "10961777702801604793"
  ],
  "discriminant": "-352552999829263681991029569532859586844198362034699175226580886764938405380171285356667243171936320073457306159450267792000000",
  "regulator": "36283142742820593232603135.64812226685178757742818290974748363391051493102652911109328068",
  "points": [
    [
      "-430974524505103086646",
      "-436504753163215553526351291217"
    ],
    [
      "-431282026217274092726",
      "-231277396558468586995386847697"
    ],
    [
      "-589113183202922650369/4",
      "53837724732704877234360722858869/8"
    ],
    [
      "10954253034071526314",
      "5547355708952212364823485782343"
    ],
    [
      "212625146290836057914",
      "4220235551257346598160495822943"
    ],
    [
      "818583279697237513594",
      "-22110736313392792819241191313177"
    ],
    [
      "-131293776961743791806",
      "6665672258516273300017730546423"
    ],
    [
      "1664752028775100357306/9",
      "113341597271154182925148689356501/27"
    ],
    [
      "482236745969274185024",
      "9495466500517104002451683117423"
    ],
    [
      "82025587408214429114",
      "-4834079480913535803044474669857"
    ],
    [
      "966089402129518336714",
      "-28732166110245761971353472434257"
    ],
    [
      "-267123365697887011486",
      "-6545076109203927028790502258457"
    ],
    [
      "155573188466321919428",
      "-4283596370597718671452804099819"
    ],
    [
      "232969447323236766914",
      "4308692958885999753855388131143"
    ],
    [
      "-352314543590275237606",
      "-5263388623451814963534649724377"
    ],
    [
      "161441249820478607114",
      "-4258485808079276265040936676857"
    ],
    [
      "321017918295087042164",
      "5398743343171957578111486434693"
    ],
    [
      "8642778609811336549694",
      "802906953069629247915774660912383"
    ],
    [
      "-423027622216463997598",
      "-1909972772688973221766525638217"
    ],
    [
      "260779767920004388814",
      "4532342077558886402747012669843"
    ],
    [
      "451891285588895981678",
      "-8584529904885921368925812210509"
    ],
    [
      "47536442803839103964",
      "-5175366294618306856583885510707"
    ],
    [
      "381710865468695045264",
      "-6699815423815473649631545474207"
    ],
    [
      "-120653594915480301826",
      "6614154015446921371465926293123"
    ],
    [
      "-369918552796879756186",
      "4773410456502860229859641728843"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 1249/283 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -25474223654459729695152T^8 + 93424157542535492313792T^7 + 249549530991798533589216T^6 - 697407234931421362933344T^5 - 624235669206688152877680T^4 - 597548430366277034810016T^3 - 3503195429735821784150304T^2 + 3443481263994739372563948T - 932157668798019061834527,\nA6 = 1558176592694379366370572668882304T^12 - 8556444096428535116807109681029376T^11 - 10909694949700311770505743225764224T^10 + 132365209573836556400929013899470720T^9 - 65939622169833360804191934552439680T^8 - 921173694379955547822888188003154432T^7 + 724370040233725908757397970764697408T^6 + 3685802165670854989077288042679139952T^5 - 921815011359411216952545051496976700T^4 - 3541405794655636698734958615621659160T^3 + 4046594122834363561792364624080217124T^2 - 1844492709789748579332256815007671156T + 328955182757185562525000064586958946.\nIt is a 2-neighbour of the fibration given 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": "2026-10-13 06:57:24",
  "updated_at": "2026-10-13 06:57:24"
}