{
  "id": 2904,
  "curve_key": "747257954773455297368569:-723537086319676251407207713653997453",
  "ainvs": [
    "1",
    "0",
    "1",
    "-15567874057780318695179",
    "837427183239068708883156864245306"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 165.13891974632008,
  "faltings_height": 11.737517736554192,
  "conductor": "21562908872242620554490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "43",
    "47",
    "59",
    "199",
    "4253",
    "200171"
  ],
  "discriminant": "-61482187436127611179256998582710011973699216285785466845330039406900",
  "regulator": "316897.5759408076962191978870332924308876377517854516",
  "points": [
    [
      "-32139533487987374/1476225",
      "61247190507620849513440156/1793613375"
    ],
    [
      "45930010734004324/140625",
      "9223935642228073786865582/52734375"
    ],
    [
      "43645757670296/25",
      "-287630941043294057946/125"
    ],
    [
      "-122934054739",
      "-29889293125883808"
    ],
    [
      "-1196861745765433/26569",
      "-164756524879427584584654/4330747"
    ],
    [
      "169560533842875589/144",
      "-69821177182803145764946717/1728"
    ],
    [
      "138308037549137641698/3575881",
      "-1626555577020812997760756378157/6761990971"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1264 via the rational 2-torsion point x=72981399279. 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 20:27:41",
  "updated_at": "2026-09-26 20:27:41"
}