{
  "id": 3038,
  "curve_key": "1160531789855012302877953168:29045659041294372890845509040287527072960",
  "ainvs": [
    "0",
    "1",
    "0",
    "-24177745621979422976624024",
    "-33617660927432101946278517493176845824"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "naive_height": 186.95602755130918,
  "faltings_height": 13.602184483922343,
  "conductor": "1605314370710886136520856",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "29",
    "31",
    "47",
    "151",
    "181",
    "313",
    "661",
    "1009",
    "3049"
  ],
  "discriminant": "416315627569180646254422946651943649242673544861505276073071062562508969452544",
  "regulator": "12754728.1889733735203215859888936732113911641919580549",
  "points": [
    [
      "-238325216411072/121",
      "3357309915766215730080/1331"
    ],
    [
      "-33871366027709/9",
      "-54467762682562326730/27"
    ],
    [
      "-11663702100779/4",
      "-27816349861671345975/8"
    ],
    [
      "-53912206060616/25",
      "364278840918621415248/125"
    ],
    [
      "-1697497574432",
      "1591435744721681040"
    ],
    [
      "1123168014724879797400/6974881",
      "-37623810604445202324554722869696/18420660721"
    ],
    [
      "117359496485816927611/2739025",
      "-1262712745944117727530500922966/4533086375"
    ],
    [
      "18512911122566561954839/189805729",
      "-2515658069338424855569414998631596/2614953528433"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z4old678-023, rational kernel x=1980591661228. Source: https://dujella.github.io/tors/z2z4old678.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 20:34:25",
  "updated_at": "2026-09-26 20:34:25"
}