{
  "id": 734,
  "curve_key": "1547888488294497141564383521:-61003261184289098313336045617026378187569",
  "ainvs": [
    "1",
    "0",
    "0",
    "-32247676839468690449257990",
    "70605626370702287593291208184391240292"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 187.82349190309915,
  "faltings_height": 13.445350289446951,
  "conductor": "642884886366548148202012413927085430843957817030186813570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "23",
    "41",
    "263",
    "16879",
    "46589",
    "547753",
    "51093698777909",
    "3926108614450504543793"
  ],
  "discriminant": "-7361616441155997504222964414994197990171646052840844529598289788910080000000",
  "regulator": "7994226767220038.8941231455108593818043346732675696419148006430438744235703",
  "points": [
    [
      "-4702387039396",
      "-10874987972282036422"
    ],
    [
      "50149499482296821/21904",
      "-9603302947727125786776379/3241792"
    ],
    [
      "2540581049174",
      "-2253021992756651812"
    ],
    [
      "3139493965274",
      "-555355557032431762"
    ],
    [
      "3237204281204",
      "-370897539700387582"
    ],
    [
      "3293257404404",
      "-350565505767537022"
    ],
    [
      "3293379750764",
      "-350616135775315222"
    ],
    [
      "3337657734074",
      "-394069144284338962"
    ],
    [
      "1001275123524386/289",
      "-3359449989091188795056/4913"
    ],
    [
      "15109077930371/4",
      "-13122583426646344421/8"
    ],
    [
      "4221242711084",
      "-3114197866199302102"
    ],
    [
      "362716079587948/49",
      "-5286094478696037899066/343"
    ],
    [
      "73516283211916/9",
      "-506726620551246448274/27"
    ],
    [
      "39903955185311/4",
      "-217875906904167853631/8"
    ],
    [
      "276956228354924",
      "-4608144921260762687062"
    ],
    [
      "942259491950924",
      "-28923305169622702431862"
    ],
    [
      "3268868141364524",
      "-186894040249292665410262"
    ],
    [
      "3350906886958",
      "-415428978238830044"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=1/4 of the family identified by wgxli in the commentary to curve #302. Starting from 17 reconstructed generic sections, minimized quartic searches produced a set of 18 points certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 17:19:35",
  "updated_at": "2026-09-16 17:19:35"
}