{
  "id": 2819,
  "curve_key": "60987060225:-14445674057534625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1270563755",
    "16719847800122"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "naive_height": 74.50178265347549,
  "faltings_height": 4.1381812962795115,
  "conductor": "41419028475",
  "bad_primes": [
    "3",
    "5",
    "11",
    "23",
    "47",
    "113",
    "137"
  ],
  "discriminant": "10508729718803655594969140625",
  "regulator": "184.691071705541576210242597292172008389318646943",
  "points": [
    [
      "28213",
      "-1838835"
    ],
    [
      "457365/16",
      "-124972553/64"
    ],
    [
      "4841349/16",
      "-10591186355/64"
    ],
    [
      "47154",
      "-7875515"
    ],
    [
      "37804",
      "-4784790"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1652 via the rational 2-torsion point x=-8541. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:23:51",
  "updated_at": "2026-09-26 20:23:51"
}