{
  "id": 3139,
  "curve_key": "59238732979986156032548251763340828421003073:-455714731826182582384171339156781967986603115424565004717483268321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1234140270416378250678088578402933925437564",
    "527447606280303914796391760482999986982123024359861103558856208"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 302.37044852102093,
  "faltings_height": 22.94599935642192,
  "conductor": "5300423313342790652288129860235660003742350867406",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "29",
    "31",
    "41",
    "59",
    "61",
    "79",
    "163",
    "601",
    "607",
    "1231",
    "1327",
    "2652103",
    "4368649",
    "823091551"
  ],
  "discriminant": "119371036414019011111138119587532608188007883235958316759444193334079961840375049684246931168480927535384463941063441322606592",
  "regulator": "293669610165.376114848156883120742920880381402912823066066128",
  "points": [
    [
      "709854151409081257848",
      "3013053332382683287650073999428"
    ],
    [
      "22744758292531540126629594936/33953929",
      "-227497543993207940466707988963366484305876/197849544283"
    ],
    [
      "586908362296483747834588152/190969",
      "13394964856000011690760045225905544125492/83453453"
    ],
    [
      "4990896667677781057426483602744/7130958025",
      "-1538061034694278823778016998444860244259466412/602173750421125"
    ],
    [
      "1062772792746641133432",
      "-20401566229736295136350415456188"
    ],
    [
      "2776691497482834086472",
      "-136047623182217818541217481035324"
    ],
    [
      "-40523127142036214257585608/32041",
      "46354443978431482597451747683995361644/5735339"
    ],
    [
      "1211429423820876546285345912/1216609",
      "-22687719208292944209843735965200336499844/1341919727"
    ],
    [
      "1305666854674964352888",
      "-33792424270074872172362806691772"
    ],
    [
      "7864353463742404222415928/29929",
      "77024420688208441252644606203221130004/5177717"
    ],
    [
      "82960197411147952439693459832/125059489",
      "-1151620588266421982802376953254272996424964/1398540265487"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-050, rational kernel x=-5224161910020248206273/4. 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 20:39:05",
  "updated_at": "2026-09-26 20:39:05"
}