{
  "id": 3133,
  "curve_key": "323203480851867715942821802652764103966594241:-4147481193809945809670606078891434761416570644063171220269532828961",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-6733405851080577415475454221932585499304047",
    "4800325455798548390824144090920449266363788590480449836501600119"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 307.460568006904,
  "faltings_height": 23.647873998132614,
  "conductor": "2329609314357493409271842921820896872147183012290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "61",
    "71",
    "79",
    "199",
    "601",
    "619",
    "859",
    "1123",
    "7207",
    "191413",
    "3560785447"
  ],
  "discriminant": "9583561190810340949965506160233081904365761537906361508834070611789094135130032823242817457223775245723594946978512896000000000000",
  "regulator": "118334321463.573146402840827289155616408227237554961878397221",
  "points": [
    [
      "50429106765918034135627/9",
      "10209853371013635306144099631896706/27"
    ],
    [
      "1375362162769333581779723763/543169",
      "25271915733559758246347818833627891635558/400315553"
    ],
    [
      "17753007070797729895507475567563/4790439369",
      "58135309193657036492499090136121538549011430142/331560680046597"
    ],
    [
      "446496888543804182065307691/570025",
      "1112404713531836154703264257824331365474/430368875"
    ],
    [
      "4268560138861462087827",
      "-232021827991116929702294289753914"
    ],
    [
      "2733669554261469467827",
      "-82595355076513411474712481933914"
    ],
    [
      "4112932438270069308147",
      "-216059075917969934152568499590234"
    ],
    [
      "-624081786012809503053",
      "93591961365784987234330897324966"
    ],
    [
      "496637464908185004906751323/11449",
      "-11048252638240567810184553779847367808302/1225043"
    ],
    [
      "15119404109271018481107",
      "-1832821949315141747883603089429114"
    ],
    [
      "150483958258821153253360347/32761",
      "-1577667833005258823329326427476197416274/5929741"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-044, rational kernel x=-16895950390905374942613/4. 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 20:38:50",
  "updated_at": "2026-09-26 20:38:50"
}