{
  "id": 64,
  "curve_key": "0:-15662988285231130964521270306488",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "18128458663461957134862581373"
  ],
  "rank_lower_bound": 16,
  "naive_height": 143.65770656998274,
  "faltings_height": 10.029131456623523,
  "conductor": "141972917837550720141347359033819641029697926227598433712323",
  "bad_primes": [
    "3",
    "41",
    "1768630113508483622913422573"
  ],
  "discriminant": "-141972917837550720141347359033819641029697926227598433712323",
  "regulator": "359787206510825092.8999100746454939974782593912647860402619044739747445",
  "points": [
    [
      "1061832153",
      "139016765771325"
    ],
    [
      "-2069581821",
      "96250143600728"
    ],
    [
      "2323084809",
      "175115687339501"
    ],
    [
      "2437726383",
      "180595326275964"
    ],
    [
      "3097225419",
      "218722516138736"
    ],
    [
      "7619958189",
      "678654480211793"
    ],
    [
      "13493940633",
      "1573274288396285"
    ],
    [
      "15245095569",
      "1887136964766261"
    ],
    [
      "6376192377/4",
      "1191407043318535/8"
    ],
    [
      "17844824169",
      "2387591696553138"
    ],
    [
      "5948344741/9",
      "3664166411156266/27"
    ],
    [
      "7271819311/9",
      "3687841575833417/27"
    ],
    [
      "-11236359299/9",
      "3434674826973187/27"
    ],
    [
      "31140274567/9",
      "6588845927720308/27"
    ],
    [
      "-26120241831/16",
      "7512202525369347/64"
    ],
    [
      "-1185892731/25",
      "16830196043015853/125"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Noam D. Elkies, \"Rank of an elliptic curve and 3-rank of a quadratic field via the Burgess bounds\", ANTS XVI. This is the minimal model (7) for E_{16D}, y^2 + y = x^3 + (D-1)/4 with D = 72513834653847828539450325493. The submitted points are the 16 independent points P_i in table (10). This is the 3-isogenous companion of the E_{-432D} model already on the board and has smaller naive height.",
  "created_at": "2026-05-29 04:45:01",
  "updated_at": "2026-07-01 22:37:39"
}