{
  "id": 4284,
  "curve_key": "23180940246819732615977153340332105425:-110375133926737988048675244474577699774237624667467536025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-482936255142077762832857361256918863",
    "127748997600391189830907215398551042650777655852973817"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 258.1091812431682,
  "faltings_height": 19.37863055070209,
  "conductor": "5084368801484321084038637605177674753072542398692670741298716815560457210693766644242550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "23",
    "37",
    "43",
    "15668111",
    "4331441340349",
    "5614534240395316891486875292563840312435116723892689583941"
  ],
  "discriminant": "158418358193986670589235343102890435042304256561129708288520797479038682826409418310332667625982065889280000",
  "regulator": "2884900720586821506487715.0560373321060476777849979816623368124311165378545498586194585",
  "points": [
    [
      "344057674201221132",
      "48157399098850269161793069"
    ],
    [
      "365221709912945466",
      "-9272727065214527762623995"
    ],
    [
      "358228012862510982",
      "-26798126085313444840165731"
    ],
    [
      "44308333318879130238/121",
      "-3595826457299508497388743553/1331"
    ],
    [
      "-593849757367745298",
      "452896218372721533670067589"
    ],
    [
      "332739710674683799872438/76729",
      "-189607948845658569459258308755551783/21253933"
    ],
    [
      "14362813898718137082",
      "-54370050415087173186962887551"
    ],
    [
      "104186148332274342",
      "280293853333664194922710269"
    ],
    [
      "25498591871836918374/49",
      "45186160866659103797561729115/343"
    ],
    [
      "117955693242776112",
      "269119116218593348853051259"
    ],
    [
      "101549964321040332348/961",
      "-8314653621554600923044262065645/29791"
    ],
    [
      "454856680685737482",
      "46793232138984628201034769"
    ],
    [
      "442197204084439722",
      "-25738204060786035059259471"
    ],
    [
      "766826159429999382",
      "-456433753372001561496866451"
    ],
    [
      "-776116664521669242",
      "-187255193680771002544594275"
    ],
    [
      "445320529230327942",
      "31610907198586956899957469"
    ],
    [
      "14020906512619276422",
      "-52437276260893388843176258851"
    ],
    [
      "-141698540750454634842/289",
      "-2440064602209834753766152281523/4913"
    ],
    [
      "-197679403769866074",
      "-464209867870406560028365731"
    ],
    [
      "215742420022958982",
      "183305338660649105999650269"
    ],
    [
      "338757341192117208",
      "-55003772172991585312712925"
    ],
    [
      "2905852298448271923/4",
      "3203033664467926181656646847/8"
    ],
    [
      "-799202118288826308",
      "56948057655928049500811469"
    ],
    [
      "1957289949861155848/9",
      "-4905345766710433456859180927/27"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 253/102 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -159593418515992752T^8 + 66594122607180400704T^7 - 9577916877180584429856T^6 + 378921666915696440595168T^5 - 8319401481873790592668080T^4 + 116272680309493432400708928T^3 - 728840755857976029224439616T^2 - 494050735965340585862790156T - 1390993922871848594371288527,\nA6 = 40790046358717726655041920T^12 - 19761746514541051225237666560T^11 + 3565895854811577447633633290880T^10 - 339557681946125505951450862243200T^9 + 23467317247680868700633154198453120T^8 - 886973909798626440691615033339785600T^7 + 17462193623232977878169289412672255680T^6 - 168744348646923648755279986373234058480T^5 + 648041970284178877886227382317646179620T^4 - 1598469487562293877807341226375296120200T^3 + 21038628236849997090209222042624669117476T^2 + 9643147208228838672635695562458112132532T + 18608807243853177902952156937051966196946.\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 17:08:46",
  "updated_at": "2026-10-16 17:08:46"
}