{
  "id": 4000,
  "curve_key": "30146853613551243724224:-5893449317463995590609680865786368",
  "ainvs": [
    "0",
    "0",
    "0",
    "-628059450282317577588",
    "6821121895212957859501945446512"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 155.5182990354328,
  "faltings_height": 10.937865067554117,
  "conductor": "1005791021107376101017459673931692686720",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "67",
    "71",
    "73",
    "137",
    "151",
    "401",
    "619",
    "1583",
    "2789",
    "4513",
    "22303"
  ],
  "discriminant": "-4244384256564033257321755973554888164941804316174226407767040000",
  "regulator": "2801463064902547.493486050669211162584173921112603274430087172078",
  "points": [
    [
      "58099898461",
      "12901660526457225"
    ],
    [
      "21428510917",
      "1789499901241773"
    ],
    [
      "34961603197",
      "5253304018016007"
    ],
    [
      "55973975713/4",
      "-7031594975637969/8"
    ],
    [
      "28518565277",
      "-3479103459064087"
    ],
    [
      "146685924313/4",
      "-46029533907481731/8"
    ],
    [
      "233908363909/169",
      "5361082053573510675/2197"
    ],
    [
      "281141922017/16",
      "-70413698128299217/64"
    ],
    [
      "3100928381/25",
      "-324596410672570279/125"
    ],
    [
      "-4505092352771/289",
      "17593476207303072825/4913"
    ],
    [
      "4846202565293/289",
      "-4924278097073207489/4913"
    ],
    [
      "5689293707301721/118336",
      "-381336546672375168700125/40707584"
    ],
    [
      "6610080458199073/3844",
      "-537358698102681303630831/238328"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3009 (source contributor: Steps Unbounded). Source equation and witness provenance are credited to that entry. Exact rank 13: 13 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:43:09",
  "updated_at": "2026-10-05 04:43:09"
}