{
  "id": 3037,
  "curve_key": "25051131895279794391615219942369:-120184712969939009316380137202480818894815407953",
  "ainvs": [
    "1",
    "0",
    "0",
    "-521898581151662383158650415466",
    "139102677048540476550558210975450499388872100"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 216.89541540531516,
  "faltings_height": 16.005022791853907,
  "conductor": "2958865796524431023234757779070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "23",
    "29",
    "37",
    "41",
    "43",
    "53",
    "59",
    "71",
    "73",
    "12569",
    "3131981"
  ],
  "discriminant": "738832923014727520277890809204373654417532918601880336543868106634446233686024282271846400",
  "regulator": "47041091.6224858328000843278835972875149535894312386238",
  "points": [
    [
      "329822230580036",
      "1687565207858244545030"
    ],
    [
      "339674215029686",
      "1009114376200243682234"
    ],
    [
      "302154232422500",
      "2999106591792166425110"
    ],
    [
      "-199734351443992",
      "-15341955029071957267834"
    ],
    [
      "29871458072000",
      "11114830612904501597990"
    ],
    [
      "-580988662510316",
      "-15691028220629492394074"
    ],
    [
      "340328699602681364",
      "198539481505542503412693830"
    ],
    [
      "97457855700918346/49",
      "28633912063299364148293828/343"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral - Tadic (2019). Source: https://dujella.github.io/tors/z6old678.html (curve entry 30). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:21",
  "updated_at": "2026-09-26 20:34:21"
}