{
  "id": 3129,
  "curve_key": "4225317153837273850066267389315477696:405591903587795865728410885950888232098332621079392256",
  "ainvs": [
    "0",
    "0",
    "0",
    "-88027440704943205209713903944072452",
    "-469435073596985955704179266146861379743440533656704"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 253.00247301532337,
  "faltings_height": 19.151647229206795,
  "conductor": "3046788250100588932752869018478456421677120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "29",
    "61",
    "109",
    "131",
    "139",
    "151",
    "163",
    "179",
    "307",
    "563",
    "761",
    "827",
    "2213",
    "11423"
  ],
  "discriminant": "43559821348587958727543495527097653641964829717039800108013721936865104442316735347698301265723393026560000",
  "regulator": "19015700335.9839829827244686497299412471723553937592342448876",
  "points": [
    [
      "209617812197080975147342121/82882816",
      "-3013885079862340766111330182111549268395/754565156864"
    ],
    [
      "-52091056290089092931808534404071/220980949623184",
      "278397794954158590696701233652691349320682910845/3284976395995068882752"
    ],
    [
      "20842880086667298533427678828722/22838831442001",
      "89955898806002004237603091670910026220836968000/109146752622491336999"
    ],
    [
      "766666300792694775867324624392808358/744757717180732369",
      "-642652378214775636971216015947389406045460833614431880/642721041445774823999503847"
    ],
    [
      "561353793239557780401823089411602/393146768429041",
      "13008707730030179683640543959585769144786843114000/7795286210990466486089"
    ],
    [
      "6901180880049671525517638368/10396453369",
      "-512336331101396170041257592488989209952800/1060053574863347"
    ],
    [
      "141366143590712356286129274105703130836054590892/41071715886486887072058600961",
      "-52953671820371066843951153057392391682689289921914963381163866733269100/8323658822543745194166422708228964275070209"
    ],
    [
      "15761045093871346955770753545673762/35509569153549241",
      "-1464503861053494484985822597362959572318813716646160/6691417139158493717119789"
    ],
    [
      "803727931968418435881106340491403623242596815246957/2617464067429145809632361566878161",
      "-5104457127689959243067454883280311493363796813412010009052070993370687310465/133912492189384223151179135679766664513017030909159"
    ],
    [
      "60765211016062192424545250923195483258702835302/24680448730642015059545339761",
      "-14869595070145130580850591286277064761749957416453927503435397553898360/3877301537879371519306749929919160360623991"
    ],
    [
      "344734670147113515642879301/108889225",
      "-6372482987054005649605897433928224542701/1136259062875"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-020, rational kernel x=587981882605635556. Source: https://dujella.github.io/tors/z4old9101112.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 20:38:39",
  "updated_at": "2026-09-26 20:38:39"
}