{
  "id": 3125,
  "curve_key": "1136223538907422263730033412763888131233:-28062211251099339237190873048714751293137202013408777641745",
  "ainvs": [
    "1",
    "1",
    "1",
    "-23671323727237963827709029432581002734",
    "32479411170253864847996755216329958698104110437129185946"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 269.7855861147477,
  "faltings_height": 20.505006317106595,
  "conductor": "5656989953868346894737119189064534826653330489",
  "bad_primes": [
    "3",
    "7",
    "11",
    "17",
    "41",
    "43",
    "59",
    "73",
    "89",
    "179",
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    "197",
    "293",
    "353",
    "433",
    "443",
    "1181",
    "2269",
    "2389",
    "2629511"
  ],
  "discriminant": "393160505905096073124817180853595652017675372111508294026768797023020288098616045745597219777293541382057983342929",
  "regulator": "724633148635.254317359380573736557578609258503919043790985666",
  "points": [
    [
      "3735369604870046796871/225",
      "-219119146931097581659186027238264/3375"
    ],
    [
      "1419369180780813229169/1024",
      "50035539819520401352479158510457/32768"
    ],
    [
      "17377249838302980740598031/106276",
      "72407047518464979439091470104220720189/34645976"
    ],
    [
      "706125819281986395038789311/488012281",
      "-12090441220491174083174609198006377369316/10780679299571"
    ],
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      "3154265868324388601501479/410881",
      "4585925489897778387670082268236452000/263374721"
    ],
    [
      "2611202057170942279981170576988/463983032569",
      "-2782409965932542725463409330862656828121560265/316048074413797747"
    ],
    [
      "-25287172410358202760635/104976",
      "-210127032384335358035509430843486417/34012224"
    ],
    [
      "1522931485637300523270329195719675261073886157331825570747896485415/114551486160991949376813174104106574629330572356",
      "-1762935125675040714113465785413168208467097084999554610446355445159073910029287898115436454420028973/38770472334254900926053753710170117893821151854168194428335882650519496"
    ],
    [
      "2004257467874308134963809506820183110665756995994304986213312320841307687/55034045011542821423623857105136389356824319174168449",
      "-2812990962686450731121016980197805840534882811886805421008906724111156921898304231917429288742872906067881808/12910621587072220361535141180555623704106882010802404046535277250371804355670207"
    ],
    [
      "36792105757070068154023089375849558292/2039496998193748921",
      "-215538575605909644475417080891711964685007852415386475727/2912625219857208513938503469"
    ],
    [
      "861845476423155632349514348771472734858439789186135814491550892365/24088345470803328858530377469994206813417721616",
      "-792953874783035143199987928715566898299924247951264101152586173750986994682184836062644285464915847/3738612525720859571942905656829310315764169694368145909539261668569664"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-017, rational kernel x=2722011719392931145. 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 20:38:27",
  "updated_at": "2026-09-26 20:38:27"
}