{
  "id": 4173,
  "curve_key": "931512042357478603456:-30535665028111431531396536720896",
  "ainvs": [
    "0",
    "1",
    "0",
    "-19406500882447470905",
    "35342204887178656570893130903"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "naive_height": 144.9928962709343,
  "faltings_height": 10.037081998608416,
  "conductor": "13767280447195777685103339403832411097298898560",
  "bad_primes": [
    "2",
    "5",
    "7",
    "29",
    "43",
    "61",
    "330907",
    "136789181",
    "892516293545548488157723"
  ],
  "discriminant": "-71840370513891307772451042284388553024762942729977472000000",
  "regulator": "143003248156445.7808323816230459406538076024216663213193179486649309246",
  "points": [
    [
      "13994577826",
      "1582583146150825"
    ],
    [
      "2959307794959/169",
      "4944338486911214860/2197"
    ],
    [
      "622576157598939/1849",
      "15532871707026579973340/79507"
    ],
    [
      "-343181002156931/131044",
      "-12388830225238632562075/47437928"
    ],
    [
      "-539228522214/121",
      "242965243114661305/1331"
    ],
    [
      "133963761779/625",
      "2759590154664084708/15625"
    ],
    [
      "210562915230799/94249",
      "1620569019612979186100/28934443"
    ],
    [
      "15350074834/9",
      "2291753724140125/27"
    ],
    [
      "12987201262209/4624",
      "17199794611192128215/314432"
    ],
    [
      "1745366481596594/375769",
      "49085910902437545724875/230346397"
    ],
    [
      "266798863679/169",
      "-204212862263347140/2197"
    ],
    [
      "12835323089469/1369",
      "-41694220779970453100/50653"
    ],
    [
      "12525943711977946/5013121",
      "-555789773290698916957925/11224377919"
    ],
    [
      "42590753203",
      "-8744555419896268"
    ],
    [
      "27596548518652279/528529",
      "-4568621735612671022370700/384240583"
    ],
    [
      "27630300786539/4489",
      "-116128012003624280100/300763"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Mestre construction: sextuple [-650, -481, 74, 225, 256, 576], T = 23; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x), p(x) = prod(x - a_i), on the locus sum a_i = 0, 12 p5 = 5 p2 p3. Found by a discriminant-first sweep + Nagao-sum rescoring + ratpoints search on the quartic.",
  "created_at": "2026-10-11 22:58:08",
  "updated_at": "2026-10-11 22:58:08"
}