{
  "id": 5564,
  "curve_key": "58346131277674544206022887316641:-444089370958103921039272456780790978664020584561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1215544401618219670958810152430",
    "513992327497805362870457801237239200960288900"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 219.43183753303543,
  "faltings_height": 16.107992390233367,
  "conductor": "99935178321411365632289509476483547017130759704544808220279106537410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "67",
    "73",
    "206519",
    "766778660971410713390790717044025393935190086891940343"
  ],
  "discriminant": "816363031892357422591851680423103400258478504127225513516856028446534975050761213952000000",
  "regulator": "78597737262880399361.028544182567955616478511155500518441073862685418611745237981",
  "points": [
    [
      "588266684209660",
      "1581854225051607522370"
    ],
    [
      "685218857862460",
      "1675017604710229751170"
    ],
    [
      "604110417137212",
      "372858780650961340546"
    ],
    [
      "1475549197150330",
      "43966230765086237584870"
    ],
    [
      "605173753864360",
      "-112843366790200282730"
    ],
    [
      "-361098030104840",
      "30097156173678450762370"
    ],
    [
      "2523332522302410",
      "-116246937357283972295130"
    ],
    [
      "73169093327928460/121",
      "347358190934553152760470/1331"
    ],
    [
      "1675548322936636",
      "-56403258682513967547518"
    ],
    [
      "717645715286260",
      "3355692034493046867370"
    ],
    [
      "909958250106460",
      "-12702951150487965593630"
    ],
    [
      "670286461881910",
      "-615073060977034046780"
    ],
    [
      "599107742166460",
      "887726794736266127170"
    ],
    [
      "1205531895051940",
      "28295279995104219770170"
    ],
    [
      "737997388532860",
      "4343585535895251368770"
    ],
    [
      "1616509558312060",
      "-52660796529334617245630"
    ],
    [
      "604878564276220",
      "-217672679974513335230"
    ],
    [
      "2819717371731100",
      "-139662188915135782464830"
    ],
    [
      "23965778709360700/49",
      "2071467565133270594979310/343"
    ],
    [
      "371963880851260",
      "10645072338144452586370"
    ],
    [
      "730201063749052",
      "-3967246457799680277758"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -87/91 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -197025213169039645478907T^8 - 341931841726476599360316T^7 + 665947206984249248496984T^6 + 768079108867411834646148T^5 - 206522586961384218063030T^4 + 567964478469951746923788T^3 - 1467887770507529603462256T^2 - 589605913192300591575636T - 60265701752223364133607,\nA6 = 36494962374013345038748480651016406T^12 + 110908265109200423180608249500271092T^11 - 159142246935958461715703643687536484T^10 - 720270176428343092357105513183159380T^9 + 221065402893902851082492835239899950T^8 + 1953863404097225126588131072937056920T^7 - 202924758161403130921394088084358680T^6 - 2477568108201452732342173930140320280T^5 + 261194239478925852479287144045333650T^4 + 771382032898538394406350724439690100T^3 + 379387733802661108189747796000121180T^2 + 80405723305695990012919388855834220T + 5982031282168624025426587018231050.\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": "2026-10-23 08:06:42",
  "updated_at": "2026-10-23 08:06:42"
}