{
  "id": 3122,
  "curve_key": "12149649293199375239110649235376012978250909008641:-42274321481042988030097316348233240443993563126269522501661327460203922561",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-253117693608320317481471859070333603713560604347",
    "48928612825281236145946031275063726668034883245591529738101538876498219"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 339.0641543049807,
  "faltings_height": 26.05004549128733,
  "conductor": "66720045390731263315331475333869520786441558783362426910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "37",
    "47",
    "53",
    "59",
    "61",
    "67",
    "83",
    "101",
    "103",
    "151",
    "191",
    "283",
    "317",
    "443",
    "523",
    "613",
    "1063",
    "1621",
    "1747",
    "2383673"
  ],
  "discriminant": "3668869303550805917697384026448682337766848072601000322829128847051741099975481846658783305595011420200893411393993319896752921344768778240000",
  "regulator": "753887898795.193143908201459638465286775322744444883760771347",
  "points": [
    [
      "418280425983058874460427",
      "127421184276024187226510211355140186"
    ],
    [
      "8276856246345306536968764361339/1274641",
      "23742677510397535405074378951136151918343766218/1439069689"
    ],
    [
      "2827023297687111812398003/9",
      "549146291730148394020487297823463822/27"
    ],
    [
      "300520540784526948650187",
      "-1528620058749285161768233412982374"
    ],
    [
      "4542160993231767616966930932123739/13807425025",
      "57629409225881756136763550761581807792329213639178/1622441477562625"
    ],
    [
      "2323088150052179069288934981633/7661824",
      "-159617382757634763863008260351496450117768903/21207928832"
    ],
    [
      "112485099459600231592247181995436647431483/175100086988842129",
      "-28512938986560886458786923043069193476770722647999152097904138/73270565387748194086567367"
    ],
    [
      "699358954749915120973123269846147/1826622121",
      "-7044379110903680222102627953030141068752927479586/78068002829419"
    ],
    [
      "3026759980001961350605545853313778179019883/9345848566798351969",
      "-867622611422269842892126128292232478534209178753328112376796218/28571175550650567916022136047"
    ],
    [
      "-1488870890822375752779100836644373/2861073121",
      "30501602744268723872071899531822638596109021973434/153035940169169"
    ],
    [
      "623651649581811709046563/9",
      "4808854753798866730882142773733126462/27"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-048, rational kernel x=-2403108265506338506958421/4. Source: https://dujella.github.io/tors/z2z2old1011121314.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:38:20",
  "updated_at": "2026-09-26 20:38:20"
}