{
  "id": 5714,
  "curve_key": "752003168143284083931236809425:-637690279687176982753764457444454149484163225",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-15666732669651751748567433530",
    "738067453341643943018542942387536851909497"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 206.37761414321008,
  "faltings_height": 15.0989119018811,
  "conductor": "55034951546964991139138083802185247323265579001352924047680717540850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "29",
    "53",
    "103",
    "56479023325919",
    "34982651027904517823",
    "5077902543976259414767067"
  ],
  "discriminant": "10772853014023705967165698312967221014304432773190189899690344066121854016462766080000",
  "regulator": "28528189218637456254.996305177380318292772976960602545568890958461462882674505541",
  "points": [
    [
      "101752141709809",
      "-444336051163277624185"
    ],
    [
      "26740056469969",
      "581599587912729185735"
    ],
    [
      "-133463527865231",
      "672074470621128051335"
    ],
    [
      "115886783655409",
      "-691975733570997026425"
    ],
    [
      "92239478389759",
      "278856335195363766215"
    ],
    [
      "55687272738289",
      "-195755231370015846265"
    ],
    [
      "280293043896274681/4489",
      "17211790013767851526072445/300763"
    ],
    [
      "-131895653437727",
      "714089338342820652455"
    ],
    [
      "43308777894049",
      "-375223325292676294345"
    ],
    [
      "85709059735153",
      "-157825765123393070329"
    ],
    [
      "81915364422809",
      "-66210539109708244625"
    ],
    [
      "36195176883049",
      "-467360973349751296705"
    ],
    [
      "91731768220529",
      "-269865309285176007545"
    ],
    [
      "860612190185569",
      "24993406321772334005495"
    ],
    [
      "62559558414769",
      "-52941661508048626105"
    ],
    [
      "-52898725525055",
      "1191130772824622089703"
    ],
    [
      "88336836891509",
      "208435151901323627215"
    ],
    [
      "38390970716689",
      "439533311652284218535"
    ],
    [
      "4123942454350639",
      "-264710432394737221607065"
    ],
    [
      "19495642054264129/361",
      "-1525976190889460175166075/6859"
    ],
    [
      "81286187567329",
      "-40895502790292085385"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 48/13 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -58701756188828782740672T^8 - 421589935203760423753344T^7 - 677464368389618755113936T^6 + 669015607734413855170992T^5 + 1311645217705022688331320T^4 + 1050713078894545198928832T^3 - 1636359720229735222434336T^2 - 2517746756775352549692984T - 810344655390742277047947,\nA6 = 5480627817022307258018449212308736T^12 + 59387395680501866438327388746270208T^11 + 202192728222021747784840349845289856T^10 + 81426836279267976104124948661760640T^9 - 731444121000417496333010776856855280T^8 - 504969396495943282941884145271012800T^7 + 1906585932510725663650827845073118320T^6 + 512612498829370479665585111044169040T^5 - 2456755728368285626110680543972723880T^4 - 642737286070578650255592249597744000T^3 + 1935352237260464424985879727209027440T^2 + 1451023268234470568001166626460852200T + 303174450039421684871841546202620870.\nIt is a 2-neighbour of the fibration given in curve#4647: 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 15:32:58",
  "updated_at": "2026-10-24 15:32:58"
}