{
  "id": 2162,
  "curve_key": "377549703271189243091536:-230983016675782422638853466626069440",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-7865618818149775897740",
    "267341454488481158401019215375716"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 162.8639675315748,
  "faltings_height": 11.401875830612537,
  "conductor": "16305275978428710457836900037023245758488",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "29",
    "83",
    "109",
    "139",
    "149",
    "151",
    "179",
    "193",
    "337",
    "389",
    "1493",
    "2179",
    "3023",
    "115469"
  ],
  "discriminant": "268638460991272988217079322143830763883844104458994380173970205952",
  "regulator": "891978093910.1004093953858943049354119214570359617516264499725200",
  "points": [
    [
      "55602654876",
      "1377100091401074"
    ],
    [
      "-71448228612",
      "21554432050780818"
    ],
    [
      "54045575208",
      "320296107012462"
    ],
    [
      "44628960438",
      "2279590425653868"
    ],
    [
      "-76780089440",
      "20460492645477654"
    ],
    [
      "2909436479644/49",
      "1065168631473771138/343"
    ],
    [
      "99203703264",
      "21525421222361898"
    ],
    [
      "-89826516016",
      "15782589431083802"
    ],
    [
      "48228019884",
      "416900491537698"
    ],
    [
      "-222630956/9",
      "441626269440877442/27"
    ],
    [
      "1710647676163602/27889",
      "18427438836769083168276/4657463"
    ],
    [
      "53764935347624/961",
      "46164683548407507118/29791"
    ],
    [
      "173734689425310738/1852321",
      "47480031389486563966337148/2521008881"
    ]
  ],
  "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; 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 14:17:25",
  "updated_at": "2026-09-26 14:17:25"
}