{
  "id": 3610,
  "curve_key": "10186401359800250211252308176:-1029406694835843296743527980937869400927424",
  "ainvs": [
    "0",
    "1",
    "0",
    "-212216694995838546067756420",
    "1191442933837710854554825439162733665600"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 193.47511303518885,
  "faltings_height": 13.905399097117193,
  "conductor": "1981462165998296003807157433092943494958225792032062040",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "41",
    "43",
    "61",
    "107",
    "274845816139948483",
    "25718962493678706481977833"
  ],
  "discriminant": "-1567647466686818845220732103888091845121404701119043310457329636069268380000000",
  "regulator": "580194262576957873402517.01302379910362778448751237126204528254311078045886",
  "points": [
    [
      "13165160258177360",
      "1510563405478808924017200"
    ],
    [
      "-36304940567158658607800395/2339988208804",
      "97981363184181491190611551282526589705/3579484642983896408"
    ],
    [
      "-278598882936376282930390/39883684681",
      "384724520348477570228384617145825250/7965130783957829"
    ],
    [
      "-41142090119275/4",
      "382503484101339649545/8"
    ],
    [
      "32123100022763005/676",
      "5513659714701843298530195/17576"
    ],
    [
      "175101962029393970/22201",
      "9527690775963263010941610/3307949"
    ],
    [
      "3658596893888296550/9409",
      "6993124352937594244440149670/912673"
    ],
    [
      "11838785270940153860/1190281",
      "10440651800873287280699982000/1298596571"
    ],
    [
      "71175575980424753135/7890481",
      "73954071696393616265549893350/22164361129"
    ],
    [
      "95841741276619442645/9947716",
      "201273642379863921949313591415/31375096264"
    ],
    [
      "125721572199910613210/16638241",
      "298322394270307642854671067750/67867385039"
    ],
    [
      "280773973956180133010/21743569",
      "2492354507670554577925928968110/101390262247"
    ],
    [
      "3255261606633082063040/736742449",
      "368752142919293442065331373516200/19997400293207"
    ],
    [
      "7325661934442800589015/693742921",
      "206706927595368116295443192745330/18272494796219"
    ],
    [
      "212690915935316167087415/24390005929",
      "7594053555700119555067217090702850/3809060395949717"
    ],
    [
      "983448458652811542513140/551860294129",
      "11731789823009407645462110618854275800/409962112280492617"
    ],
    [
      "2852201812711710234347840/329938806409",
      "323749172826712402541058577734095400/189517840217748827"
    ],
    [
      "13074696596775087275776345/3123306874944",
      "107093194274175038524493399232821224835/5519782760406031872"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 13 of the rank-17 fibration of X1092, y^2 - (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #1393 (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 19:18:48",
  "updated_at": "2026-09-29 19:18:48"
}