{
  "id": 5675,
  "curve_key": "696326754301198220523927868321:-579951859966600974242475296245260081578672881",
  "ainvs": [
    "1",
    "0",
    "0",
    "-14506807381274962927581830590",
    "671240578665046214991138708851770018156100"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 206.1468496067269,
  "faltings_height": 14.976409836834174,
  "conductor": "517651166534074019469670472013472623378510068018601453452444490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "167",
    "8111676714902938322307449879",
    "95771699980783885624756201807"
  ],
  "discriminant": "743318358355526061372998256112710837958291722570286269395395985955532047506160000000",
  "regulator": "4415827662192088784.93220084036519787665834063794501373239021842303966387261062",
  "points": [
    [
      "76238163284780",
      "-91564595985709285390"
    ],
    [
      "64601969198480",
      "60688064918654331410"
    ],
    [
      "66051955918550",
      "34829143919498891060"
    ],
    [
      "41606499434780",
      "373748758209182350610"
    ],
    [
      "55920709925660",
      "-186763798090792741870"
    ],
    [
      "20658882128780",
      "616735870775366644610"
    ],
    [
      "-123536603484700",
      "760285575246925124810"
    ],
    [
      "99204286585880",
      "456531596048774473010"
    ],
    [
      "63733712801780",
      "-74520779888370625390"
    ],
    [
      "484606351332740",
      "10365698574738197844650"
    ],
    [
      "5498145151683380/121",
      "433100883219134392836910/1331"
    ],
    [
      "77838377282696",
      "-116886321352525087738"
    ],
    [
      "30990780239571740",
      "-5455637322834745963537390"
    ],
    [
      "33210494995340",
      "-475490718631516741390"
    ],
    [
      "55190627660630",
      "196752921067123758260"
    ],
    [
      "76468184703596",
      "95237225690184132002"
    ],
    [
      "88180062911780",
      "278734916257460713610"
    ],
    [
      "1876961191700",
      "802507616905666441490"
    ],
    [
      "3183326210358260/49",
      "-18742690654113221564770/343"
    ],
    [
      "137496629271980",
      "-1129611355186568677390"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -65/41 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": "2026-10-24 05:25:12",
  "updated_at": "2026-10-24 05:25:12"
}