{
  "id": 3653,
  "curve_key": "3366035485644361996069147221532561:-194177962771283712905529736400125425666718446825145",
  "ainvs": [
    "1",
    "0",
    "0",
    "-70125739284257541584773900448595",
    "224743012466763550759810773071275962457173164961"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 231.59713112068366,
  "faltings_height": 17.140957306798438,
  "conductor": "2050943799731838770795008718676624626173063235165279006502",
  "bad_primes": [
    "2",
    "3",
    "11",
    "47",
    "137",
    "167",
    "179",
    "293",
    "307",
    "353",
    "433",
    "439",
    "1193",
    "1697",
    "2647",
    "4787",
    "5393",
    "10211",
    "20161",
    "26863",
    "34961"
  ],
  "discriminant": "250437983262427361284766549940053429335781466528186256238429284746113038429474020987452918218752",
  "regulator": "15324107086174751135.10100142294253329388275312204698776390111076470537",
  "points": [
    [
      "4011125375232078",
      "89416913858436189809529"
    ],
    [
      "6576372845569758",
      "219064937612195671731273"
    ],
    [
      "20693955204040404",
      "2763247892048250754871955"
    ],
    [
      "101814396335978814",
      "32380710357493942041363225"
    ],
    [
      "1768348194780203985/64",
      "2254042173260881531239849213/512"
    ],
    [
      "6661029569181270834/25",
      "17183040655816079582336464713/125"
    ],
    [
      "7140827896366670526/1369",
      "1500999993494766220087386165/50653"
    ],
    [
      "14304799441228871058/1681",
      "34060039425423379190003026329/68921"
    ],
    [
      "14678575361306770758/3481",
      "13018372123599098657811079971/205379"
    ],
    [
      "18076771028524845598/81",
      "76803271743698979341113018817/729"
    ],
    [
      "322330764564225228540/9409",
      "5628086295050009828955380074473/912673"
    ],
    [
      "164548871336383594449456/28058209",
      "18315428816338941065096354853878223/148624333073"
    ],
    [
      "516542169431021749047642/114340249",
      "14541921904075744266251065549375761/1222640282557"
    ],
    [
      "3416375559827424969684606/759829225",
      "384845062875762659866079899322823501/20944692587125"
    ],
    [
      "20377855121971249896247182/2999424289",
      "40871033643489795133236697377701434839/164269470035663"
    ],
    [
      "598946995332182445750772854/112766341249",
      "1742280565256025560591922699365082985623/37867726755802943"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -971/167 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 19:27:27",
  "updated_at": "2026-09-29 19:27:27"
}