{
  "id": 745,
  "curve_key": "791488309163376497498329121394528778000:-22130435451521048669564741431202601582171534666307345009600",
  "ainvs": [
    "0",
    "1",
    "0",
    "-16489339774237010364548523362386016208",
    "25613929920741954473166448583590674302293472150393717988"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 268.7009353695464,
  "faltings_height": 20.236150151280906,
  "conductor": "9252467452476159857081397435096950329303577724136752038772152521917883645245369769040427481200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "47",
    "71",
    "101",
    "665384696019408514388819",
    "747023040411454510195699",
    "9857528942884130812331333025182357"
  ],
  "discriminant": "3515417228832982492329928296324410223992511163996413555036738271741064785181095671456611579715879770046833280000",
  "regulator": "5519807073021843845879008.30169833212536154084933988776187368473375637471529351446117",
  "points": [
    [
      "-1634362246264492722",
      "-6942468870763540819471040880"
    ],
    [
      "996254020109771418",
      "-3189853129309052080503977820"
    ],
    [
      "1765557752902092288",
      "-1415851189864345822793680470"
    ],
    [
      "1843142222932715754",
      "-1217869047783228832757035356"
    ],
    [
      "2176754143087178022",
      "-186320390093194151335226112"
    ],
    [
      "2189408618032776558",
      "-83544178339163105110942080"
    ],
    [
      "10133805900376268661273/4624",
      "-15590820477211366767485604483579/314432"
    ],
    [
      "2500581670112044152",
      "-129992235860218052402005722"
    ],
    [
      "3451625416216673297751/1369",
      "-13119052919174815319713169283582/50653"
    ],
    [
      "2711974193085279882",
      "-917226635122052366791791132"
    ],
    [
      "178661910817532517642/49",
      "-1281783419819844597729683135940/343"
    ],
    [
      "4067271018630868038",
      "-5082414204084045526330296720"
    ],
    [
      "4132832456951993162",
      "-5296818529871385234965636508"
    ],
    [
      "39396369459739067998/9",
      "-164922414729999438824062806176/27"
    ],
    [
      "5152324515803640992",
      "-8799512188662219173110026198"
    ],
    [
      "6985441099347841578",
      "-15852220912926771286494790620"
    ],
    [
      "8153019903270669114",
      "-20811568444776558483111944604"
    ],
    [
      "305379508227563800073568893358/15507471841",
      "-165418385031077625253704425273005551933862080/1931129960887889"
    ],
    [
      "32337159207680902512",
      "-182502328383054701820873350442"
    ],
    [
      "2519632362730008163017/64",
      "-125827432672560226517064348539685/512"
    ],
    [
      "218226015730735421898",
      "-3223184162543500841886601573020"
    ],
    [
      "1508929761406622728917/4",
      "-58610911728423938773486766403465/8"
    ],
    [
      "66805243169880876255469/36",
      "-17266916340536774471424801198618571/216"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-16 18:31:23"
    }
  ],
  "commentary": "Specialization T=57/85 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 23 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 18:17:19",
  "updated_at": "2026-09-16 18:31:23"
}