{
  "id": 733,
  "curve_key": "196421602929044163474751174801:-95663739479294480854946946338360922442502201",
  "ainvs": [
    "1",
    "1",
    "1",
    "-4092116727688420072390649475",
    "110721920693626166311255762161035719685985"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 202.5388264691918,
  "faltings_height": 14.84560321394976,
  "conductor": "1863758222087171211274812966805615163460265969143252914506159374764670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "29",
    "31",
    "3906657554604290739885947623090224418297883612623798396578899"
  ],
  "discriminant": "-910487017029411054460720427405483502710087627078532886223610114324812102227046400000",
  "regulator": "14034576273191480333.0919549616405694755926702995816898962686930855754613055748",
  "points": [
    [
      "-284059328390393/4",
      "-1662528880525264969961/8"
    ],
    [
      "-18880592383436243/289",
      "-1547588454223506075346196/4913"
    ],
    [
      "-59966681299287",
      "-374796211356730610242"
    ],
    [
      "-59899555795157",
      "-375394265881813959802"
    ],
    [
      "-54096058422278643/21904",
      "-1126787910369638595643181589/3241792"
    ],
    [
      "13309824488003",
      "-242104157129123841762"
    ],
    [
      "29337736818403",
      "-126172711317081650242"
    ],
    [
      "36983402524963",
      "-99831803598946430242"
    ],
    [
      "3341271432900595/81",
      "-80229194980434290379410/729"
    ],
    [
      "47731852346233",
      "-155391489063345215842"
    ],
    [
      "50112183248133",
      "-177483209887680289642"
    ],
    [
      "317638540462123",
      "-5555070620003287164082"
    ],
    [
      "945068986338883",
      "-28988564551859637244642"
    ],
    [
      "1232240233907843",
      "-43198629422350091235042"
    ],
    [
      "5146515210275827/4",
      "-368759968428337122601811/8"
    ],
    [
      "2917677888666883",
      "-157562397722586680164642"
    ],
    [
      "5608933607874883",
      "-420041636038373995084642"
    ],
    [
      "29783439862833",
      "-123548007763095492192"
    ],
    [
      "30700339502083",
      "-118439665864725801442"
    ],
    [
      "34060610434423",
      "-104194541351936854042"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=-7/12 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 20 points certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 17:18:16",
  "updated_at": "2026-09-16 17:18:16"
}