{
  "id": 449,
  "curve_key": "2207306868713983086077006388620641:-73128988545806378342655908569115088417728999260561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-45985559764874647626604299762930",
    "84640033039127748879277321178403309377568768900"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 230.33124368934253,
  "faltings_height": 17.22184504749393,
  "conductor": "11106328920975712642031651694736605793017517811417688175832290165042008870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "43",
    "61",
    "71",
    "51893",
    "7222702441",
    "37089253978986320869559544323368382227544182957607"
  ],
  "discriminant": "3128819174937008750747092070091173185332512185826818190669176860413746229895787257077955072000000",
  "regulator": "35580190380997350319.7316495500701916000885705473164554683237387284360685461456",
  "points": [
    [
      "5734795874849160",
      "-97609093234795677248130"
    ],
    [
      "1502746203307260",
      "-137582625111736499564130"
    ],
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      "-1711663581811740",
      "397915849167082179687870"
    ],
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      "31654157020656900",
      "-5508721937726902853547330"
    ],
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      "78841691012769540",
      "22057651178124792518681790"
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      "-7292367207508290",
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      "5682672382142160",
      "82633941050953526091870"
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      "1582581912395460",
      "-125808577595529492291330"
    ],
    [
      "1809091016961540",
      "-85841609034492870390210"
    ],
    [
      "33216639614275236",
      "-5933512668799896612187458"
    ],
    [
      "2015294951188950",
      "12268382050821533353170"
    ],
    [
      "-3005449573404900",
      "-442379821831059527404770"
    ],
    [
      "20008355951153700",
      "-2678539895078416250054370"
    ],
    [
      "6421739058968820",
      "232716878971138779296910"
    ],
    [
      "5995117009297860",
      "156282713843277159567870"
    ],
    [
      "1529452986314820",
      "133734879463466125734270"
    ],
    [
      "-5533413661825788",
      "411911897195008870103742"
    ],
    [
      "2011543218432240",
      "16655682195695686551090"
    ],
    [
      "15576533162048500/9",
      "-2731657001660230837855910/27"
    ],
    [
      "-6476418174195708",
      "332888743790694849258942"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -3/7. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 20.",
  "created_at": "2026-08-30 15:55:02",
  "updated_at": "2026-08-30 15:55:02"
}