{
  "id": 4188,
  "curve_key": "536359884115957797716791475498050468934601:-231453706427695772517216251008408236102250681428431603334569349",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-11174164252415787452433155739542718102804",
    "267886234291314551527349387137650516425898429477051887088860"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 288.2568719643682,
  "faltings_height": 22.064166716978878,
  "conductor": "3804257995298578259616917826902327465995028217058588411971726342268947602255635322783133001109035897530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "31",
    "43",
    "67",
    "127979",
    "346259",
    "352501065480894646588728187",
    "582631398291353308547458494022671980775866631962413807"
  ],
  "discriminant": "58292954798080612901244548857378740130624488912401805971881859209276663674676063504678827502263527489417238142041654562500",
  "regulator": "45837057303746887049943376771.4726039677296897834178345643811978265155543242528268815913233",
  "points": [
    [
      "218345110680003348046",
      "2870117620671745632727060067302"
    ],
    [
      "355647576303775733521",
      "-6424793856517688830586928375848"
    ],
    [
      "459164482702694885059/4",
      "-5644362304258849506737652451459/8"
    ],
    [
      "878500304218221667246",
      "-25854307581900822040748872037498"
    ],
    [
      "91129017299984263171",
      "79852050414653270297038189402"
    ],
    [
      "103444994459580074446",
      "467895276793377682950570880102"
    ],
    [
      "164830788141920044121",
      "-1704217921460981223190798862873"
    ],
    [
      "1355828420211149139946",
      "-49774464364648723776318845072798"
    ],
    [
      "146858726726108049439/9",
      "-8095278376728952809682465433671/27"
    ],
    [
      "112504415673278386310839/529",
      "33344451743615197448380677610881629/12167"
    ],
    [
      "3083083848866894420371",
      "171089978592903940632001201025002"
    ],
    [
      "-66976424403008679554",
      "-846076936462398490256438932298"
    ],
    [
      "10148603828176173755569/529",
      "-2994569785772130588103692734450536/12167"
    ],
    [
      "495575772520885001539/25",
      "29093046216635148491918599177703/125"
    ],
    [
      "959991438223526971219/4",
      "-27022646344725170112914632051639/8"
    ],
    [
      "1012503270715721628940",
      "32045822980386150078549546958210"
    ],
    [
      "-20997501465219085459",
      "702323337030034170564954423087"
    ],
    [
      "187481797388029736821",
      "2182386558373399034222366707852"
    ],
    [
      "21162673899231152356",
      "202210111385274405875046336382"
    ],
    [
      "-111574783770483793354",
      "-354477441866296031677630643348"
    ],
    [
      "199264709738091774514/9",
      "-4779666270894580466956334301796/27"
    ],
    [
      "25410502756338949366",
      "-18775064246356971332793262178"
    ],
    [
      "95248063389407253316",
      "260149184822003029052222138662"
    ],
    [
      "4330905560062787772301934/29929",
      "6713156400568311888219497992931533884/5177717"
    ],
    [
      "357436855422593654986",
      "6476137424093133202495209037492"
    ],
    [
      "-74252069698295234650241/676",
      "7247782584880008672832512421486427/17576"
    ]
  ],
  "submitter": "apkorte",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-12 00:42:51"
    }
  ],
  "commentary": "Specialization at T = -257/517 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -113946597679617331526187T^8 - 628704898397157619416528T^7 - 910139814353468861642484T^6 + 13879376823678260295456T^5 - 533762798296920925528530T^4 + 1639003787601085356814224T^3 + 806892413125232101174956T^2 - 592355532948433669282752T - 295458143973808062849867,\nA6 = 15882493844523546552540807840095910T^12 + 145809795943145321517489625166050800T^11 + 489200782557326126999832807296770620T^10 + 474439873253302462549441686771960000T^9 - 939321256931213164482716468158448790T^8 - 1775504390224299025107326496664527360T^7 + 1396226578858524162480471413923945800T^6 + 1631143206019716771050709031938957120T^5 - 432541045559235732878122118765459190T^4 - 878384718510400823408137143448720560T^3 - 116676491482650081744926274060252324T^2 + 185829851435689714140802850197329216T + 61035568685910358648726719363207174.\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": "2026-10-12 00:38:22",
  "updated_at": "2026-10-12 00:42:51"
}