{
  "id": 3117,
  "curve_key": "1051506734295092748637832195996924364320932225:-7848020654726998946280474637067225145689301199189172321244865026625",
  "ainvs": [
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  "rank_lower_bound": 11,
  "torsion": [
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    2
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  "naive_height": 310.9996599160119,
  "faltings_height": 23.981579229776727,
  "conductor": "16491334853285711166878253103438065925189351213350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
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    "79",
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    "241",
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    "41465951",
    "58252159873"
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  "discriminant": "637166811450579847049863154899461031443294269288512139411311648743825665452320750695923645292037122182041251122502454119169600000000",
  "regulator": "32196768437815.2172461087908158507092076069603469131400937354",
  "points": [
    [
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      "-9160229283544001469019920261349557185492302580507333021444563446608790710182993880/1607693626975598516941442741328583893482025110884139"
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  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-008, rational kernel x=2437698274691638852112. 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 20:38:03",
  "updated_at": "2026-09-26 20:38:03"
}