{
  "id": 245,
  "curve_key": "1242259750673056662437665286001:-1388157434854180878311718734402758619153189001",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-25880411472355347134118026792",
    "1606663697747901005185875883284420820193259"
  ],
  "rank_lower_bound": 20,
  "naive_height": 207.88861293214381,
  "faltings_height": 15.133214475051384,
  "conductor": "272066437942638823321634957004224153562929337633497250319389959310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "37",
    "7770053",
    "763973980372286963203",
    "55722582408764114465841769948159"
  ],
  "discriminant": "-5737429639444055753512327119829925015713334222025694979826677816527336990079139840000",
  "regulator": "4687798591445119467.32292703579184309810358227475172994834982074863674547612846",
  "points": [
    [
      "45492869957717",
      "723492619381097668641"
    ],
    [
      "103561597049417",
      "192731719560345258741"
    ],
    [
      "111830641498667",
      "333174093470012383491"
    ],
    [
      "316677539205677",
      "5016853361860584594681"
    ],
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      "92008168616117",
      "65953506306453213441"
    ],
    [
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    ],
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      "213774572035037",
      "2417332168050319812441"
    ],
    [
      "81536578719167",
      "196306066193578043241"
    ],
    [
      "294423088161917",
      "-4416891036870168333159"
    ],
    [
      "227707758469997",
      "-2742321749648483486439"
    ],
    [
      "94836710011277",
      "-72195187870086062919"
    ],
    [
      "132211123753677",
      "704277531895181059641"
    ],
    [
      "91603447091117",
      "-67755953909555099559"
    ],
    [
      "60334338604917",
      "514603898948192002241"
    ],
    [
      "82129229001677",
      "-187361656905064421319"
    ],
    [
      "20079468981897",
      "-1046467649553400314559"
    ],
    [
      "107362804572947",
      "256157490251353593441"
    ],
    [
      "305606512192501/9",
      "-23646417837002335990141/27"
    ],
    [
      "1413476686249589",
      "-52811301360597927383607"
    ],
    [
      "3892455620987453/49",
      "78262410657484049671263/343"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Rank-20 at naive height 207.89: Mestre-family specialization T=5801/160 found by wide-denominator vectorized sieve (n>20 window), certified via famcert3 with base-point injection.",
  "created_at": "2026-07-07 01:03:48",
  "updated_at": "2026-07-07 01:04:58"
}