{
  "id": 3114,
  "curve_key": "118825658665882337674418272926105370264361272225:-38565722914077380067786995353251272205929372847412521726384893101876625",
  "ainvs": [
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  "rank_lower_bound": 11,
  "torsion": [
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  "naive_height": 325.18195965112767,
  "faltings_height": 25.045629018405634,
  "conductor": "326885688138289438101160708711925723710232867288025",
  "bad_primes": [
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  "discriminant": "110213147510288112580184857157721285003593504394456318327356453600820794646540484137734842402735522211005690062577763285038916521156640625",
  "regulator": "425342752621.707133941384786602167187116134779284551866583310",
  "points": [
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      "-2345256422619202616675545088328299198177630409345854432481124304515370587619329249633840302658445029690238790344925257665497781082267426500906026797830023/2639852907916014767048762195433338546420972038316540051273366982663302070684907933707541408377236346850171774965037709671"
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  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-019, rational kernel x=28537664503990119507945. 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 20:37:56",
  "updated_at": "2026-09-26 20:37:56"
}