{
  "id": 6277,
  "curve_key": "22235273995312088256:-104966387939148558816186172800",
  "ainvs": [
    "0",
    "0",
    "0",
    "-463234874902335172",
    "121488874929570091222437700"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 133.64687538976762,
  "faltings_height": 8.914792022598629,
  "conductor": "28727321523343960013176244938377167208719311048",
  "bad_primes": [
    "2",
    "19",
    "43",
    "231328685847967210052633551330100231984147"
  ],
  "discriminant": "-14269894784219785321105115205709720530590395692739328",
  "regulator": "1212419187242462.53755069457123480688155647891712378676743875219080379063",
  "points": [
    [
      "346673814",
      "1600525102594"
    ],
    [
      "107954313658/9",
      "-35414007407238934/27"
    ],
    [
      "215135133554/841",
      "108329424439601606/24389"
    ],
    [
      "658210730874/1225",
      "-225705835551359318/42875"
    ],
    [
      "256187933816/625",
      "-10819794544230886/15625"
    ],
    [
      "1060512780926/5929",
      "-3040433222253829382/456533"
    ],
    [
      "59216161425/121",
      "4610039690451785/1331"
    ],
    [
      "4109950274593/5184",
      "5931671824120230991/373248"
    ],
    [
      "105914093344/81",
      "30508748958777506/729"
    ],
    [
      "287105466",
      "3486772758338"
    ],
    [
      "311732838",
      "2716013190494"
    ],
    [
      "379065352",
      "600574351942"
    ],
    [
      "387492922",
      "413519282242"
    ],
    [
      "403715762",
      "523297000942"
    ],
    [
      "413700433",
      "807730323719"
    ],
    [
      "846057650",
      "18308058138130"
    ],
    [
      "35358007896/169",
      "12759521050362098/2197"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 17 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_17.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:38:09",
  "updated_at": "2026-10-31 23:38:09"
}