{
  "id": 4305,
  "curve_key": "27431407815616:-143088860324109007360",
  "ainvs": [
    "0",
    "1",
    "0",
    "-571487662825",
    "165611916360720039"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 92.82812923049673,
  "faltings_height": 5.5630019188405555,
  "conductor": "7623567598977423232",
  "bad_primes": [
    "2",
    "17",
    "47",
    "89",
    "257",
    "769",
    "2801"
  ],
  "discriminant": "96772201011560422077652346359980032",
  "regulator": "204809245.39118502379563956792896015500825025209114504527",
  "points": [
    [
      "1051954",
      "-853542137"
    ],
    [
      "4126882",
      "8251832159"
    ],
    [
      "6533893/4",
      "15159092407/8"
    ],
    [
      "514042",
      "87598829"
    ],
    [
      "341436106/9",
      "-6307809818239/27"
    ],
    [
      "81026026/169",
      "-93828774911/2197"
    ],
    [
      "41187322/81",
      "58736402101/729"
    ],
    [
      "1998634",
      "-2647081493"
    ],
    [
      "7622857/16",
      "-2462829389/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve#4242, submitted by Michael Rubinstein and sourced from his elliptic-curves-by-rank repository. This isogenous curve has the same rank and conductor. The nine supplied points were transported from the source curve.",
  "created_at": "2026-10-16 19:17:36",
  "updated_at": "2026-10-16 19:17:36"
}