{
  "id": 4221,
  "curve_key": "2859440958657475571686508831210296795860001:-4746220107637008386046423302197595330963452187856690380379491249",
  "ainvs": [
    "1",
    "1",
    "1",
    "-59571686638697407743468933983547849913750",
    "5493310309765056002343723952555166972425698346785431891678867"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 293.2776001274227,
  "faltings_height": 22.332157907686135,
  "conductor": "12155956057816879775291315106720585954250504860071696639621525101430862242096977971482880863570610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "37",
    "53",
    "73",
    "137",
    "108447949",
    "581664289",
    "1391773349",
    "7906300695696131",
    "77640198694120627",
    "828825525916519930703423"
  ],
  "discriminant": "493828221918437963313966250978932684552232315170943953955173177196344015469135302530975649727286178931928374742039040000000",
  "regulator": "739569374363533190534254173.407444773379971979512593765532871464421318525594844622554364101",
  "points": [
    [
      "309146429441221758937",
      "4077073540700166220890968235031"
    ],
    [
      "249050171898397561697",
      "2470739669736873353691490630191"
    ],
    [
      "81356811069207926257",
      "1088688637662779071233384805551"
    ],
    [
      "76107956786838251137",
      "-1183334395326554726849514218769"
    ],
    [
      "175576624067202781337",
      "-668162979975660701945683654569"
    ],
    [
      "124431745452084988937",
      "-85500519467475337014679953969"
    ],
    [
      "211309388432013553505",
      "-1529891534352181666760702964177"
    ],
    [
      "-236692163658198173063",
      "2516587758179129705861618615031"
    ],
    [
      "-126082020752649311163",
      "3316616334958893129957410277931"
    ],
    [
      "252445072221077277937",
      "2557866496892491791575403258031"
    ],
    [
      "176565438477501605537",
      "-692458950274858557616290449169"
    ],
    [
      "7807875129385929763937",
      "-689587692278799098522826931509969"
    ],
    [
      "157581890558304548705",
      "137742668118975682186499647023"
    ],
    [
      "161183033535454589937",
      "-280883549939933581290970103969"
    ],
    [
      "-203245988488922967583",
      "3033997686653066260358199700911"
    ],
    [
      "48768793526901447784913/49",
      "10471975384161998476471341550584633/343"
    ],
    [
      "57783700819653412319337/361",
      "-1665672688929770421400084638384251/6859"
    ],
    [
      "13859370346787831115437",
      "1631354489776667614398628541114031"
    ],
    [
      "-142174065302646783583",
      "-3330019324993493117712013555089"
    ],
    [
      "90789152268818985077",
      "-912793743314758601087935105329"
    ],
    [
      "172506920057805699917",
      "591906259186978346159384919171"
    ],
    [
      "4227218139790884894361/25",
      "-63100242862584495891004118255949/125"
    ],
    [
      "235300596497616163337",
      "-2122215107919815360002859255769"
    ],
    [
      "662636837703332856187",
      "16030424849657823328494693456531"
    ],
    [
      "19162157382388080677153/169",
      "-973790700969194026545112487949693/2197"
    ],
    [
      "165230606069182087257",
      "-401535189745173477659778558449"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 1050/61 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -9474380172051378777648T^8 + 143016499424841795151776T^7 - 978479134779758056367040T^6 + 1264156022749661958710016T^5 - 1005963702085547848031760T^4 - 1438422958271309512308048T^3 + 2172965217056038418681880T^2 + 1222317589612619797944408T - 1528603489372304441232027,\nA6 = 356599201940399174539163794687872T^12 - 8095747446508036482913060524583296T^11 + 84031424784510859456436955014577216T^10 - 395756683659861170554655745272982720T^9 + 1041818162127380294010702794653004496T^8 - 91848543443162490589835301473411808T^7 - 1400855594533976892297125576033331840T^6 - 623560771669003657652924198286452928T^5 + 1801926810925269265387912620705751296T^4 + 1152132793779120258533624208322687440T^3 - 1448000646205536545177160777048329016T^2 - 809134531551941303559229668814825224T + 723128597502954965566093502187696054.\nIt is a 2-neighbour of the fibration given in curve#4205 (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": "2026-10-14 09:37:01",
  "updated_at": "2026-10-14 09:37:01"
}