{
  "id": 737,
  "curve_key": "133833490723908474315908467650481:-1549745624487735511995469787169125135050283910121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2788197723414759881581426409385",
    "1793687065379323276904205672808349144893035225"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 221.92435053588716,
  "faltings_height": 16.26527538176486,
  "conductor": "5745932247948358625427592409401576733924557139961681884130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "41",
    "43",
    "47",
    "73",
    "109",
    "677",
    "14781515860297024393923302273753248669831"
  ],
  "discriminant": "-2642292438436287213148380446452007902821930673897011865401810864366417566514934133760000000",
  "regulator": "1208539094260698.6678052057807066955390484300271894133596467748318402859428",
  "points": [
    [
      "-713381263593198",
      "-58478082757389016040709"
    ],
    [
      "3329251562949351255/5476",
      "-7285771391108797322851954515/405224"
    ],
    [
      "836557549313370",
      "-6829792043680539074685"
    ],
    [
      "940321719625620",
      "-1822442167041629960685"
    ],
    [
      "945324049880762",
      "-1647355406941330103293"
    ],
    [
      "963743140504410",
      "-1306168293010428542685"
    ],
    [
      "965287287566010",
      "-1307746557996676778685"
    ],
    [
      "973222885786560",
      "-1396327879788502081125"
    ],
    [
      "977102800693050",
      "-1483409956239836933565"
    ],
    [
      "985241675888970",
      "-1736003150446671632685"
    ],
    [
      "296460090212182980/289",
      "-17695600376198324629499655/4913"
    ],
    [
      "1111169848673370",
      "-8214956032724660738685"
    ],
    [
      "1226549530846620",
      "-14801172950675508806685"
    ],
    [
      "2148913785114890",
      "-75666440569264995165805"
    ],
    [
      "952385864680863670/441",
      "-707994290524670467220336785/9261"
    ],
    [
      "2349147544733370",
      "-90595565630196461738685"
    ],
    [
      "74422708723681370",
      "-20297839588627594758402685"
    ],
    [
      "8526249269068679050/9",
      "-24896389168196431920311130095/27"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=4/17 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 18 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 17:40:55",
  "updated_at": "2026-09-16 17:40:55"
}