{
  "id": 314,
  "curve_key": "252478992480086640286464784:-4011164400926338562179321386414530364352",
  "ainvs": [
    "0",
    "1",
    "0",
    "-5259979010001805005968016",
    "4642551389959286676185695447422235620"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 182.38011083703807,
  "faltings_height": 12.907933281346173,
  "conductor": "145855597016413173717093065412472683801352457871296529840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "59",
    "2069",
    "23831",
    "176592536225594123223340949652953524751227"
  ],
  "discriminant": "2890929371722789110949306313392128089803170966886362237901259169725260800",
  "regulator": "1654927905997430702.5093919430042470480632172338368733749155977929860404374",
  "points": [
    [
      "-16482328548576198/6241",
      "166379936565244843857780/493039"
    ],
    [
      "-5659979172803466/2209",
      "-118314679144771907074368/103823"
    ],
    [
      "1002460149787152",
      "-31739460502428886506390"
    ],
    [
      "-168478746384816/121",
      "-4051796527631485983714/1331"
    ],
    [
      "176401596607977/16",
      "2295792302138269065405/64"
    ],
    [
      "1307309331072",
      "19970243846526870"
    ],
    [
      "5784286914353409658/4297329",
      "-307657994676127822433814380/8908363017"
    ],
    [
      "33062664429861486/24649",
      "-83048351311764662106192/3869893"
    ],
    [
      "1282304475825052911/982081",
      "24282311042834950983886554/973242271"
    ],
    [
      "836450562392319/625",
      "141404588723156471622/15625"
    ],
    [
      "1440824533313913552/1100401",
      "-13784437241185352260583610/1154320649"
    ],
    [
      "1275537803232",
      "92439705229956630"
    ],
    [
      "2712748775247",
      "3215071393107043470"
    ],
    [
      "1264895703582",
      "-114063632905141920"
    ],
    [
      "2781129678474",
      "-3394852297697850444"
    ],
    [
      "315746253262272/361",
      "-5783762931973896222990/6859"
    ],
    [
      "1377682472664",
      "-104039547001445094"
    ],
    [
      "-2010826486553238/841",
      "45953449007909090473020/24389"
    ]
  ],
  "submitter": "Christopher R. Hill",
  "commentary": "Found with Rank Hunter v0.7.17;  rigorous rank lower bound >= 18.",
  "created_at": "2026-08-24 01:58:08",
  "updated_at": "2026-08-24 01:58:08"
}