{
  "id": 6004,
  "curve_key": "1698080178537962531437460378354137681:-2207531067951467600418163809378193724791901757442298329",
  "ainvs": [
    "1",
    "0",
    "0",
    "-35376670386207552738280424549044535",
    "2555012810129013423461855950892650379207999062397097"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 250.26768496187427,
  "faltings_height": 18.6615953041324,
  "conductor": "2104871013643958885399236871022985406085174767280449508928964787218548041758610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "47",
    "59",
    "83",
    "163",
    "241",
    "2663",
    "9712731331",
    "109618608364842654238983000805193366395233621421111"
  ],
  "discriminant": "13414653947308735616180691060034653324080080129684632659072712124687133451985010829712315689268684800000",
  "regulator": "9702062839560899066813.73854858693154339205545026864797267758263377346080912758388916",
  "points": [
    [
      "84677136692450284",
      "-12906244331369113417967867"
    ],
    [
      "54688706200715014",
      "-27997757879643237270070427"
    ],
    [
      "125489260168447414",
      "-9579643556677052874814187"
    ],
    [
      "355201412813009134",
      "-186558936896700927360335867"
    ],
    [
      "140892605970528214",
      "-19170866096226584887397387"
    ],
    [
      "118770725757807334",
      "-5360736024273885720308267"
    ],
    [
      "5571684846760627036/49",
      "552061136274680199752613139/343"
    ],
    [
      "-87954876531657026",
      "70612599890037595542060253"
    ],
    [
      "57129273578768644",
      "-26840738072732119419853337"
    ],
    [
      "252067791815064334",
      "98252838270947843307412933"
    ],
    [
      "60421410218951254",
      "-25260399221986886747670347"
    ],
    [
      "82814331924133974",
      "13902368877468279481643253"
    ],
    [
      "833726931416726566/9",
      "230380803555039107400081271/27"
    ],
    [
      "151482568288632694",
      "-25925463323971455674450507"
    ],
    [
      "119067657434106214",
      "5552518709928895749990613"
    ],
    [
      "318526972287806374",
      "-153636437280230296542840827"
    ],
    [
      "-75886824816932426",
      "-69300924768219816859359947"
    ],
    [
      "-1336766796955946",
      "51012751149364322354589493"
    ],
    [
      "137703098604351862",
      "17166291820106300748413365"
    ],
    [
      "118615373654384034",
      "5259991322869431893518833"
    ],
    [
      "114956931622484134",
      "2717762531147970237801733"
    ],
    [
      "62237239272659284",
      "24379106511517786798326133"
    ],
    [
      "15948406373632165414/121",
      "17955232852005940607457660623/1331"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -181/119 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -16161338919951574537347T^8 - 183967925781776423843232T^7 - 306908503380230554874889T^6 + 1321820887548439573004394T^5 - 1089630203923766659668705T^4 + 1528127126557525645958556T^3 - 1325190033898795951823799T^2 - 1776684907545050991600198T - 509996388400821572993532,\nA6 = 794074859864541402077984985828990T^12 + 13480216201562664173283363261525120T^11 + 58813044515050204101637768724085915T^10 - 27005959952131974781942342196787600T^9 - 297164658623174446064912117521429860T^8 - 610242665718369417817232061166604040T^7 + 2737840349733935589023201371120885290T^6 - 1476924630602948597826251203809007800T^5 - 1760224581565992882116105923868957910T^4 + 421401656201140614180762210583159560T^3 + 1429992029749290001354466937891106371T^2 + 752996037739894365105522529181137224T + 139570007340666087279594607715201844.\nIt is a 2-neighbour of the fibration given in curve#4191 (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": "2026-10-27 18:38:16",
  "updated_at": "2026-10-27 18:38:16"
}