{
  "id": 6032,
  "curve_key": "248507386296758440752544237776:-128250064250376152210584764353568992952250560",
  "ainvs": [
    "0",
    "0",
    "0",
    "-5177237214515800849011338287",
    "148437574363861287280769403187001149250290"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 203.12511178155654,
  "faltings_height": 14.847586958737494,
  "conductor": "10212414370950124838379458948202235823276715824958296988385360304738363048",
  "bad_primes": [
    "2",
    "7",
    "19",
    "71",
    "163",
    "181",
    "948862559",
    "5388459680707",
    "45525586073389",
    "148008663822918394680161869"
  ],
  "discriminant": "-637312762280484527356370666621879265840821821714320133997788111246658282840480753408",
  "regulator": "2268261938315035911248.8644377141930198161828808747167260142323149321004977320671",
  "points": [
    [
      "31530678981767",
      "-128619817181290622768"
    ],
    [
      "206409289398998",
      "-2806035126160113976184"
    ],
    [
      "53288776900345",
      "-154508064009273029930"
    ],
    [
      "52489913452977",
      "145960881524727095582"
    ],
    [
      "50700623039021",
      "127581619259460320282"
    ],
    [
      "413533131013191",
      "8290092559270750589312"
    ],
    [
      "48865187330022",
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    ],
    [
      "136889225348582",
      "-1415927341482198819932"
    ],
    [
      "34764790531569",
      "-102315239464882833886"
    ],
    [
      "42788868848663",
      "72464105848602794984"
    ],
    [
      "-74643394251037",
      "344961284113203971984"
    ],
    [
      "-1198646066160767/16",
      "21782917786280757811649/64"
    ],
    [
      "7836510920021",
      "-329161579793068339282"
    ],
    [
      "94269307425881/4",
      "-1590243681661381592293/8"
    ],
    [
      "142291847428497/4",
      "-770795133639351883553/8"
    ],
    [
      "1511277050911541",
      "-58685756355433076920462"
    ],
    [
      "22488006135077",
      "-208288864673720755582"
    ],
    [
      "233399623464253/9",
      "-4800827360639573792486/27"
    ],
    [
      "436715856126908449/4624",
      "222763378430557324669005361/314432"
    ],
    [
      "43709918327978",
      "75174777989578199366"
    ],
    [
      "242461505451137/4",
      "1915525681457431726697/8"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -19/2 of the rank-17 fibration of X1008 given in curve#3594. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-28 14:17:14",
  "updated_at": "2026-10-28 14:17:14"
}