{
  "id": 2825,
  "curve_key": "536728563460589668865118943691041:-12434614298309373104888175072085030034795184698161",
  "ainvs": [
    "1",
    "0",
    "0",
    "-11181845072095618101356644660230",
    "14391914697117329050689039214352461501292556900"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    7
  ],
  "naive_height": 226.0891370461253,
  "faltings_height": 16.397109867324573,
  "conductor": "24793869011550390621870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "31",
    "43",
    "107",
    "113",
    "40739",
    "1257437"
  ],
  "discriminant": "-105742529383568800503063422492036847927767530545199958403226680613448816451555164160000000",
  "regulator": "83685.4050946712070857534543859067117171411212021",
  "points": [
    [
      "-50212338713940",
      "-122283501274174214105430"
    ],
    [
      "1494991187264172",
      "31881939944292796642986"
    ],
    [
      "1933393961761860",
      "230632595187600474570"
    ],
    [
      "2937317706484836",
      "83005881436952963158602"
    ],
    [
      "469571691228966885/16",
      "319772096187718923698671605/64"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Eroshkin (2009). Source: https://dujella.github.io/tors/z7old5.html (curve entry 6). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:24:07",
  "updated_at": "2026-09-26 20:24:07"
}