{
  "id": 1493,
  "curve_key": "50798716255042259891032188172838209:11379028976238533535986511821926439997825476403016223",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1058306588646713747729837253600796",
    "-13170172426202006495584011810752117863858516970224"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    12
  ],
  "naive_height": 239.7395374574958,
  "faltings_height": 17.82265518194139,
  "conductor": "65007264191559690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "37",
    "53",
    "73",
    "46817"
  ],
  "discriminant": "928398818468668188108514896780636116842464433931163709180134366671356343085767927738949151437619200",
  "regulator": "6753.3391553032421924618318979362060517810293",
  "points": [
    [
      "-92121435166264210827826244/4774948201",
      "85099329625362703754030041798231544612/329953695637301"
    ],
    [
      "120398019842532778115000/516961",
      "41344645335914874078954410629625116/371694959"
    ],
    [
      "-21398787345132318894636424/1127012041",
      "10631533798591302479595284142147596492/37834921228411"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/12. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 00:37:19",
  "updated_at": "2026-09-25 00:37:19"
}