{
  "id": 3191,
  "curve_key": "122872657123755172771248205611601:-2231774920332236615148766858157005477245850877401",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2559847023411566099401004283575",
    "2583072824458606980138635616347507315247155625"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 222.65376332200657,
  "faltings_height": 16.590425626362844,
  "conductor": "159345113070803533282965684718748208769606387290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "61",
    "73",
    "79",
    "101",
    "149",
    "263",
    "421",
    "547",
    "701",
    "757",
    "2719",
    "3863",
    "406591"
  ],
  "discriminant": "-1808869227102027526818691586465214543912783913685197936388516424895492022913699671703552000000",
  "regulator": "5061724094928447.86536846476778683914809190455666274531200012614206",
  "points": [
    [
      "2317987475995054950/2809",
      "4784053020734564720290045425/148877"
    ],
    [
      "-135359718875820650/169",
      "-141011684907674424239578775/2197"
    ],
    [
      "990481658847361084150/96721",
      "30827484657361108654844033030675/30080231"
    ],
    [
      "1564003630309154522230/815409",
      "50637818982549047203807602996035/736314327"
    ],
    [
      "12521158632781366482550/9690769",
      "1141830772288763694365372086986125/30167363897"
    ],
    [
      "23134829071213419850/537289",
      "-19584739648005483648083747184275/393832837"
    ],
    [
      "-1816988081087082791610/1261129",
      "81116176945161752083269522228855/1416247867"
    ],
    [
      "46946934498530237350/674041",
      "27139235822539997024780869989425/553387661"
    ],
    [
      "-72345105882333397532250/53304601",
      "-23211849321560017917796276200734175/389176891901"
    ],
    [
      "224205620575457611653325963774870/278778321916912129",
      "-4757158129935260714004968426763696651090404887285/147193454981092656875482367"
    ],
    [
      "410226844347958499517298342150/361790109849961",
      "-232176526066635477043164430894976406189525575/6881530447422051039541"
    ],
    [
      "31650312470782155581959218538450/6876638052697009",
      "-169452486715975319212977089925043397650679641175/570248628209011661738473"
    ],
    [
      "441293673628728942208090/156225001",
      "-261182136159175522519925568980089025/1952656287499"
    ],
    [
      "-74277356605452482449548042542645/116409713995387684",
      "-2498318450497054024789950446564633240809743828215/39717676424444422001441752"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-071, rational kernel x=15742887693283151/4. Source: https://dujella.github.io/tors/z2old141516171819.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 20:41:57",
  "updated_at": "2026-09-26 20:41:57"
}