{
  "id": 3641,
  "curve_key": "451283803503568165180028220361:-301432948237375864462405070389803722433183109",
  "ainvs": [
    "1",
    "0",
    "1",
    "-9401745906324336774583921258",
    "348880727126591652241550711849023093044968"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 204.84568178547565,
  "faltings_height": 14.911766933894963,
  "conductor": "4858903795077400145101018027817292162914370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "37",
    "67",
    "103",
    "229",
    "271",
    "631",
    "643",
    "1093",
    "1103",
    "1193",
    "1237",
    "1489",
    "2293",
    "19843"
  ],
  "discriminant": "604927931528949936064851119231614985252709167711692665837745219425184361390826562500",
  "regulator": "395948805867751535.538982065881636893081713441714736536539309333691",
  "points": [
    [
      "-6676247798144744711/63001",
      "6229025367045041504342558005/15813251"
    ],
    [
      "-72214492395752789/6724",
      "369299250156721340786162915/551368"
    ],
    [
      "-1167627466509864/49",
      "256536795112284919436665/343"
    ],
    [
      "25544700705016921/289",
      "2243001664415180277007315/4913"
    ],
    [
      "10808796856962554776/305809",
      "41675766241034160853367466935/169112377"
    ],
    [
      "26421245072990246569/1918225",
      "1251762649011620470492654132627/2656741625"
    ],
    [
      "77334535112489949289/3236401",
      "2161845307037460567778027721845/5822285399"
    ],
    [
      "312851945351432706699/6105841",
      "616680903014484491197103214455/15087533111"
    ],
    [
      "1246214398715912318662/19562929",
      "7964356572081712584179289201611/86526834967"
    ],
    [
      "43818955091918019033094/736525321",
      "213986702670965002895520971372420/19988560686619"
    ],
    [
      "510784333803417111889039/118243876",
      "364962174369734534205151606297221745/1285783907624"
    ],
    [
      "2900435326518811421392564/64262757001",
      "2091547048069415367054766669647757280/16290673162510501"
    ],
    [
      "7748059194553642502332054/20759334561",
      "20901273315800323948733455483662913805/2991025682883441"
    ],
    [
      "14556310661252676628478931679/38294673216361",
      "1703871622227946118508152135682376852586045/236977739129937069109"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 18/271 of the rank-9 fibration of X400, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #802 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:25:13",
  "updated_at": "2026-09-29 19:25:13"
}