{
  "id": 2161,
  "curve_key": "11160598622648512467616:-7403561644885282956530493458355680",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-232512471305177343075",
    "8568937089065100171604611728196"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 155.9745385131744,
  "faltings_height": 11.055302240332566,
  "conductor": "16305275978428710457836900037023245758488",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "29",
    "83",
    "109",
    "139",
    "149",
    "151",
    "179",
    "193",
    "337",
    "389",
    "1493",
    "2179",
    "3023",
    "115469"
  ],
  "discriminant": "-30915840540606445218989989935518049344204033623134155623607435568",
  "regulator": "792869416808.9781416847874616043870328190729208548903346221977955",
  "points": [
    [
      "16249234573",
      "3013502396427597"
    ],
    [
      "20443767113",
      "3515669204543543"
    ],
    [
      "9341135709809/49",
      "28475798228503744217/343"
    ],
    [
      "-14007336155667/676",
      "37243524039386054337/17576"
    ],
    [
      "-420108929044/25",
      "347554794426211804/125"
    ],
    [
      "36794258273",
      "7058790390506897"
    ],
    [
      "-9833207324939/441",
      "15125563866075893369/9261"
    ],
    [
      "5186594277",
      "2739071478604725"
    ],
    [
      "1389781809",
      "2872016685288513"
    ],
    [
      "-24198398815",
      "160285889604689"
    ],
    [
      "-26109467354047/6889",
      "1752666947419516602035/571787"
    ],
    [
      "381609639136",
      "235567598473036134"
    ],
    [
      "44133778572156/961",
      "289985277247041964464/29791"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Z/2Z curve from the Elkies-Klagsbrun rank-9 family y^2=x^3+2A(t,u)x^2+B(t,u)x (Elkies-Klagsbrun 2020), fibre u=29/13, t=-1/7 (the 2-isogenous partner of that fibre); one of the smallest fibres of the family (|a|,b<=40 over 8 values of u), rank certified with PARI ellrank: 13 independent points.",
  "created_at": "2026-09-26 14:17:21",
  "updated_at": "2026-09-26 14:17:21"
}