{
  "id": 4669,
  "curve_key": "530370449990599967721:-12219294855497983759687072932981",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-11049384374804165994",
    "14142702381810938408153672208"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 143.16113807553427,
  "faltings_height": 9.671774831074098,
  "conductor": "28770513284662855740810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "29",
    "37",
    "41",
    "61",
    "101",
    "157",
    "487",
    "499",
    "1627"
  ],
  "discriminant": "-70468927605301820107969942746781526333517727784179687500",
  "regulator": "397465713.58890375478916996958116074927082912436706743452",
  "points": [
    [
      "9206559951473883/4853209",
      "31307944407363051847428/10691619427"
    ],
    [
      "1691313581417418/877969",
      "2026156416393671640792/822656953"
    ],
    [
      "3408469183998/2209",
      "2875617980735103972/103823"
    ],
    [
      "52727974679007/27556",
      "11156044445260773669/4574296"
    ],
    [
      "2624668788393/1369",
      "121831377791656617/50653"
    ],
    [
      "55738191363265902/14280841",
      "9420723679374010231812546/53967298139"
    ],
    [
      "960322626118983503488/477794765529",
      "2425265894690232442309819837612/330264642392314083"
    ],
    [
      "-15883280681628498/17048641",
      "10820592349766961549333996/70393838689"
    ],
    [
      "7686643382714196928/3079473049",
      "7857439205748301205440874748/170889197908157"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Exact rank 9 established by Magma 2-descent. Independence also checked using a 10x10 mod-3 reduction matrix including the rational 3-torsion point, with determinant 2 mod 3. Found by a precomputed Mestre–Nagao sieve of the rank-5 C3 K3 deformation, specializing w=7/4, t=81/64.",
  "created_at": "2026-10-20 19:31:14",
  "updated_at": "2026-10-20 19:31:14"
}