{
  "id": 5885,
  "curve_key": "363640138203083644128172241425:-218857520674290594029480307051115719057045625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-7575836212564242586003588363",
    "253307315595243111769991900955612878239217"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 204.19788677444248,
  "faltings_height": 14.814845524043973,
  "conductor": "122665703982197592918011353225269391857219002944296150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "31",
    "53",
    "89",
    "224859416301016411986025200151559732884973"
  ],
  "discriminant": "108235107828445772707094291004294804784295270446847402880717944841353119739904000000",
  "regulator": "375263394431834.60477379930909094192335244666223408501252535328500655097319",
  "points": [
    [
      "203329086840062",
      "-2668163601983226732031"
    ],
    [
      "47898498053402",
      "-18111914936181196051"
    ],
    [
      "41330066571902",
      "103906006002551371649"
    ],
    [
      "46253405103902",
      "43041673850808156449"
    ],
    [
      "24526660291262",
      "286795280877189559169"
    ],
    [
      "-95091103932598",
      "-337428373086472058851"
    ],
    [
      "44557562433842",
      "64884892210939512329"
    ],
    [
      "55444711510142",
      "60915807820789126529"
    ],
    [
      "30707033691902",
      "222778333866821256449"
    ],
    [
      "86145109933886",
      "489864435298537019009"
    ],
    [
      "54223386247502",
      "44114602698841985249"
    ],
    [
      "48399985972862",
      "-4093262065761976831"
    ],
    [
      "-98364234477898",
      "216271334953308959249"
    ],
    [
      "208147812886142",
      "2773900424797162659329"
    ],
    [
      "-26694227761282",
      "660694036462762677377"
    ],
    [
      "100851852517118",
      "-717665772519283092223"
    ],
    [
      "58448006542142",
      "100911251313281662529"
    ],
    [
      "176221662540542",
      "2095395214318256028929"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -4/21 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -8921224827903176421867T^8 + 94634723251967943349008T^7 - 153371039643193058472636T^6 - 641050270990816586343840T^5 - 1411956329363864664615090T^4 - 3616744002660872511746400T^3 - 276286449215617413614716T^2 + 3264390669786107213517648T - 1094619040863704280589707,\nA6 = 270621608798713355418362188083174T^12 - 4440334258578316878189533038482864T^11 + 26574225298655897363019125632965972T^10 - 44466546059753405576217220076774400T^9 - 266551804859294565919720379747154006T^8 + 857066304185931807663129817734860208T^7 + 2882807104710383577362230811059875192T^6 + 490875434163168933481957024140491568T^5 - 2474513386731796364719321202224339446T^4 + 1633690238596691275986648934120443840T^3 + 1554365531979876509922013707743895892T^2 - 1882445996339364406394564636163936624T + 453429930884494956186985826996791494.\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": "2026-10-25 19:39:29",
  "updated_at": "2026-10-25 19:39:29"
}