{
  "id": 4280,
  "curve_key": "40236656193353787057771339494734621441:-255440571757545571582189288628845911383591829186632335489",
  "ainvs": [
    "1",
    "0",
    "0",
    "-838263670694870563703569572806971280",
    "295648809904566633705826741132887998607563449009873152"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 259.76516961681347,
  "faltings_height": 19.41339342309082,
  "conductor": "1087082323124172970804700960653831711732174870850503116296359589462243941425852611957958270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "29",
    "103",
    "32341",
    "188159",
    "701629",
    "6336451867",
    "23295658112341",
    "3186684232608907",
    "66377124816574825306552483363"
  ],
  "discriminant": "-62038182325295515245525043587379882577889341723004194550221798927482954679027231232148652381616223680000000",
  "regulator": "11875510971711546190803686.947822306128798340342150300358129417513378322337440097354284",
  "points": [
    [
      "450135901719031144",
      "-97590070664492191315157072"
    ],
    [
      "1183673181395391394",
      "980735442560534736401744428"
    ],
    [
      "-514905077886240776",
      "768608918229306950214770608"
    ],
    [
      "1556095110685815694",
      "-1661086782501013435126951172"
    ],
    [
      "540099366249334144",
      "21309016686172532317554928"
    ],
    [
      "3293193538819169596/9",
      "-5257123631769833483690589044/27"
    ],
    [
      "-132681059029128896",
      "-636030478105372687241975312"
    ],
    [
      "93408716061834766912",
      "902735080177903126755969752560"
    ],
    [
      "529912990908061384",
      "-15674516904000033423660152"
    ],
    [
      "650841307475068144",
      "160514561280104059501026928"
    ],
    [
      "565257377594983144",
      "49222017778736174869869928"
    ],
    [
      "-21386755706022356",
      "-559970327852991671003214572"
    ],
    [
      "483530372008775644",
      "58077964457200034526899428"
    ],
    [
      "8960503153219272829/16",
      "2745577936015554461734604617/64"
    ],
    [
      "431635259968694944",
      "-119340626644037679595214672"
    ],
    [
      "355327548202166944",
      "-206527146414712157254478672"
    ],
    [
      "531931833869906254",
      "-16142359096224404238001412"
    ],
    [
      "138256143025808370979804/143641",
      "33581489416804097870619948526986892/54439939"
    ],
    [
      "-923135413436773232",
      "-531792331602456759458127104"
    ],
    [
      "414383205933767344",
      "139433098291239415527676528"
    ],
    [
      "546675497184576064",
      "-27691411099041031947812912"
    ],
    [
      "331641571795101184",
      "-232640715252552249336000752"
    ],
    [
      "516017073359089984",
      "22185083773644189254845648"
    ],
    [
      "520135533447116944",
      "-18869599335684926993238272"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -709/119 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -70781753951590292657527T^8 - 367565467671631265368148T^7 - 564938152357888095468709T^6 + 861671225097878262924926T^5 + 883290795135789128496595T^4 + 1492235942354111474368304T^3 - 390179707279847183534299T^2 - 1933866828077577012667322T - 753991179760473695494012,\nA6 = 7240259042863556427532625579222554T^12 + 56530289701184340202303695554449444T^11 + 163263464615793597915652884274103291T^10 + 33336026591601761367769399981188740T^9 - 608655863176039416519152300146091520T^8 - 922975179177849633814913734492373280T^7 + 1471644379398400596650029609789831050T^6 + 1259508950348326801233446624368517040T^5 - 1608259867492513771432473315149086770T^4 - 1344292356731452517237148523695223300T^3 + 750512254493731351508294582787338435T^2 + 986666108581324895487891684114883660T + 253245346808298629177743261916441680.\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": "2026-10-16 14:16:27",
  "updated_at": "2026-10-16 14:16:27"
}