{
  "id": 4180,
  "curve_key": "17092326107099621547091501800303681:-2476702928414890453932638828633190114405054648141921",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-356090127231242115564406287506327",
    "2866554315295012188481604526135980412403718460079"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 236.6775359080052,
  "faltings_height": 17.69453646489482,
  "conductor": "128193526569028459166374822630126753659900004577719871983094272591432307462010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "37",
    "3697",
    "23663407",
    "198249931250467",
    "96409577270404055114686836277336024794067823"
  ],
  "discriminant": "-660055060273705897610566351284372804613153197366972995183781092154096453883865283195084152832000000",
  "regulator": "10516418279746969986848.6665837235103133454345870996947836330288298678164699601154561",
  "points": [
    [
      "10654893080705287",
      "-531100211467447987451794"
    ],
    [
      "19748893291391587",
      "1880587074382947880590206"
    ],
    [
      "108194569281523447/9",
      "15348038279585522255067226/27"
    ],
    [
      "17495333288726707",
      "1411285738658064619863806"
    ],
    [
      "-20705463468839813",
      "1167389173052977933587206"
    ],
    [
      "-13122047917405013",
      "2297765221624098152439806"
    ],
    [
      "8530900525691587",
      "-670545997197072668009794"
    ],
    [
      "-21012439805623853",
      "1035088927064065441681406"
    ],
    [
      "60191676162828547",
      "14124787240803003641938046"
    ],
    [
      "10452695869389187",
      "535258860321913917102206"
    ],
    [
      "11135220629968387",
      "531133817472486535374206"
    ],
    [
      "32394529927353007",
      "5032512492451564393286306"
    ],
    [
      "9321858570350467",
      "-597640779022162460751874"
    ],
    [
      "23133040030709263/4",
      "-8002479617216468849683877/8"
    ],
    [
      "107582328711330887",
      "34780897636981722437124206"
    ],
    [
      "10576632046654087",
      "532425150388326750468206"
    ],
    [
      "4051646839459087",
      "1220784201486365605548206"
    ],
    [
      "1169896948174590043/121",
      "-761701870176456496763575142/1331"
    ],
    [
      "1977908286526155803/169",
      "-1207570290367833695061177418/2197"
    ],
    [
      "809419343305987",
      "1605882429060876196743806"
    ],
    [
      "8643411434619602467/841",
      "13188519513292426483529645134/24389"
    ],
    [
      "454543597174442917",
      "-306193087871887132977447094"
    ],
    [
      "-21349183474536413",
      "-859123920640160914097794"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -29/96 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -6490299971789709696747T^8 - 122171843220159373604496T^7 - 507701052166171299717636T^6 + 1050551383991494297232448T^5 - 1535498496547466925264930T^4 + 2182465350304253473007088T^3 + 607653974805791446562364T^2 - 1786833563705739775293696T - 740288204118893840150907,\nA6 = 301250623701631052997714872966886T^12 + 5692055598226519603489686839092272T^11 + 35336888180450378093651037180173676T^10 + 117205369002705497808649348735832160T^9 + 178701654202460409889459615037185530T^8 - 1878311915395808086196582818654473120T^7 + 1979838463701093911232660031750203240T^6 + 1153701456205174682023944677522475360T^5 - 1378053281785187552098745035715906070T^4 - 1354630698351600468048880643107976400T^3 + 348278788638126247479431301650393100T^2 + 854663677517493018162704474754865920T + 245812677073686954605814171513689430.\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": "2026-10-11 23:00:07",
  "updated_at": "2026-10-11 23:00:07"
}