{
  "id": 2943,
  "curve_key": "-65996819011224783290357672917280283830144:-70154219729159633397244717322887864139363388196723867429734496",
  "ainvs": [
    "0",
    "1",
    "0",
    "1374933729400516318549118185776672579795",
    "81197013575416242358380437774253718563779553511837441125828"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 284.81160307465615,
  "faltings_height": 21.798864652571236,
  "conductor": "4508790919021502851120376724936227453340",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "37",
    "41",
    "47",
    "59",
    "67",
    "97",
    "113",
    "491",
    "577",
    "8287",
    "15325760017"
  ],
  "discriminant": "-3014507510792456345676525711044093915272769411641743885472791321556086843554899158473519540437047416997093604660452750000",
  "regulator": "966487163.780496456761120676682277148844549710338387593",
  "points": [
    [
      "13050589888772022503401/576",
      "4867548429454720644199199337831275/13824"
    ],
    [
      "1103154487921204503",
      "-287602365034188870243708642057"
    ],
    [
      "-32967425917925634624",
      "-6188879061380464310621855550"
    ],
    [
      "-177118811291355697132311/29584",
      "-1372473530103474925375086970804276605/5088448"
    ],
    [
      "946565168977663762209/784",
      "-6318928275680364661795653618121575/21952"
    ],
    [
      "-2961734911603264776072099/90601",
      "-989791471799361771464151377057615175/27270901"
    ],
    [
      "619968963985707879833719776549/108904620049",
      "-10734282571624695485538982560390199254749644275/35939286948510343"
    ],
    [
      "-32861552494431952299",
      "-22977591285876174222339235275"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-057, rational kernel x=65951374575037388855. 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 20:29:27",
  "updated_at": "2026-09-26 20:29:27"
}