{
  "id": 2941,
  "curve_key": "21596432778285567863951406971560629026301529:-100362651835622677188788769364722938796442366972295765435048060893",
  "ainvs": [
    "1",
    "0",
    "1",
    "-449925682880949330498987645240846438047949",
    "116160476661600320820319878143004063014637083173424102420727556"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 299.3433061729439,
  "faltings_height": 22.53240989951655,
  "conductor": "1677463821752304934698337236145168971930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "29",
    "37",
    "47",
    "61",
    "67",
    "71",
    "139",
    "409",
    "461",
    "467",
    "617",
    "1297",
    "298023589"
  ],
  "discriminant": "24289451110987625023862427826771956438895085379792514010614818751375454605447515713681370106273981336814703886328528236980",
  "regulator": "10000596066.9425366472539586613928691009957529608702088",
  "points": [
    [
      "318413273180740146632591/676",
      "51955146227966948577486758991353757/17576"
    ],
    [
      "1150629815422306532729",
      "-33493846191407521736385841355508"
    ],
    [
      "17951377187512237894834210333961/46238761024",
      "-288640412264517167239711984751737848230348079/9942813260512768"
    ],
    [
      "408215406416605293342089396/1050625",
      "43881676831307244782315405505136328619/1076890625"
    ],
    [
      "5733727140257291537636146709/11262736",
      "164970788241859877865861067226086622341617/37797742016"
    ],
    [
      "104408587905502417781978081465381825/268850065635904",
      "148171354285328663134170970200685902851069583625749/4408239891008814049792"
    ],
    [
      "354337415641150212071",
      "1106258848750662910638941237592"
    ],
    [
      "-1500887335769872430957644800237955901/3282689294278564",
      "2829319793995243338113154755320366358730749457947162509/188080888704881108967512"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-036, rational kernel x=-193404925306860615997. Source: https://dujella.github.io/tors/z6old678.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 20:29:20",
  "updated_at": "2026-09-26 20:29:20"
}