{
  "id": 1928,
  "curve_key": "91609591149605069899456792805281:874088484314181880997358324885139174687142353679",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1908533148950105622905349850110",
    "-1011676486474747706495075288533268546148531900"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
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  "naive_height": 220.78526628868048,
  "faltings_height": 16.21550716454708,
  "conductor": "74554275095325030485358128944757956425405342640170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "47",
    "73",
    "79",
    "97",
    "127",
    "149",
    "193",
    "241",
    "281",
    "331",
    "1279",
    "95617",
    "314467",
    "707563"
  ],
  "discriminant": "2769715403821110065464819901764196639923207041938771381658551546118740676549377011865856000",
  "regulator": "35232768111818.30408522549427735448045047337740517428632582192753",
  "points": [
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      "289503837623185793020957246580606680565607/3389249005855243712"
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      "-2784500314909542093220/3644281",
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      "92234245757785275337780676677973797737941499843938183438395648775205576460770931841298359344290/51909027903344538498809167114427100468483556415094026425791603577537884377"
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      "7501612205052727702200/3286969",
      "481181295577691400712571864299230/5959274797"
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    [
      "-19706370502391586232577221444647871986544821890760/24120546710350672082802829608964129",
      "-5627944427593798253125307253104388157267087786776363321230220127118481270/3746111682249571115446035671514914828140431248076367"
    ],
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      "-1348907309573219783845929999561934547241164624786614258441177866755528989367089829/1630420969406675746670906402923592730001782802709147876339266040100",
      "2105257210730550791191187066456211284686774931722891832226293190641692052726485228284603896487355046249360332421209820711/2081850928262377484771927505797382589849524732025994358498166941999065199414839747390755173980649000"
    ],
    [
      "-1020486110058820869667605385346303923088522461563202866227519105940/1231549479810945180242465790442089602552976157407769",
      "39436532235648260375986818990926156966285058942894549911798138181899112078609645823918070143783110/43219306877987062284060221435132245118586093363650979992324190691256410729603"
    ]
  ],
  "submitter": "Alvaro Lozano-Robledo",
  "history": [],
  "commentary": "Rank exactly 13, torsion Z/2Z: 13 independent points; 2-isogeny Selmer bound 13, confirmed by a second 2-isogeny descent. Specialisation of Kihara's rank-8 family (S. Kihara, Proc. Japan Acad. 77A (2001) 11-12) with u = (s^2 - l)/(2s), (p,q,s) = (1,9,161/3).",
  "created_at": "2026-09-25 19:16:47",
  "updated_at": "2026-09-25 19:16:47"
}