{
  "id": 5016,
  "curve_key": "1008597131026352526257270484487852849681:-32021486159876884668550838283641028589834444933834470220921",
  "ainvs": [
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  "rank_lower_bound": 12,
  "torsion": [
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  "family": null,
  "families": [],
  "naive_height": 269.4281370387401,
  "faltings_height": 20.18482204070638,
  "conductor": "1253778194392952346874803106376685813163046898570",
  "bad_primes": [
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  "discriminant": "369319790027770947389635016402517429873487513014697810840017161750894603463083272358993052421326499190976000000",
  "regulator": "92586911930861.931281079595667542130210669681201877284342150086",
  "points": [
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      "384733269805476932153059670/25999801",
      "7220433413984267661907285120748844396835/132572985299"
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  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 4675/8693 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-10-21 01:47:23",
  "updated_at": "2026-10-21 01:47:23"
}