{
  "id": 1924,
  "curve_key": "144151114255609589828278416:-34361079507066385415093191586236961590464",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3003148213658533121422467",
    "39769767947993501637839342113700187026"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 186.67548628188345,
  "faltings_height": 13.614110748551498,
  "conductor": "785713583551212949496355574586236811508456240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "29",
    "67",
    "211",
    "241",
    "337",
    "433",
    "479",
    "1117",
    "1181",
    "1237",
    "1637",
    "1789",
    "16253",
    "2034421"
  ],
  "discriminant": "-681532633395214059646622978148552569586592272696037882869886557847911223680000",
  "regulator": "1938148103456.109795538895289431348778403124930591194661615212888",
  "points": [
    [
      "444736605302228557/361201",
      "-1337102688125678802586983360/217081801"
    ],
    [
      "39844637988085",
      "251350881219660263616"
    ],
    [
      "-2424597658883",
      "5726934199482483600"
    ],
    [
      "5281419597255849565/1841449",
      "18489596476221430608876080688/2498846293"
    ],
    [
      "-2498701011970",
      "5627884220649718004"
    ],
    [
      "4901629494826357",
      "343171089791001979503840"
    ],
    [
      "12460730024703037/3721",
      "1861611474585164225838480/226981"
    ],
    [
      "5860696183777",
      "-14948946893043763740"
    ],
    [
      "2764385557057",
      "7252093904057712540"
    ],
    [
      "-2732464349983",
      "-5251113878460355100"
    ],
    [
      "8519948894462",
      "25152379159784227220"
    ],
    [
      "3015215238517",
      "-7624141144045869600"
    ],
    [
      "41012346297070",
      "-262487875416090955344"
    ]
  ],
  "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) = (5,4,250/1).",
  "created_at": "2026-09-25 19:15:59",
  "updated_at": "2026-09-25 19:15:59"
}