{
  "id": 234,
  "curve_key": "132982987554056065566569689:-1533719646351654702612989035132442317213",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2770478907376168032636869",
    "1775138479573443551078307813696866276"
  ],
  "rank_lower_bound": 19,
  "naive_height": 180.4570291062703,
  "faltings_height": 12.739300626770472,
  "conductor": "121367195540260815785780563003076660369683539545326996733038410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "7662261289645586443997884141",
    "4436864266498037047431696210593"
  ],
  "discriminant": "-325021758664267435353269545802736616838357964735913965003055852319441700",
  "regulator": "715538233792403396.6191825552383393257158767106899353176103967820819382092534",
  "points": [
    [
      "939237708948",
      "-39562762581743552"
    ],
    [
      "1128794739009",
      "-293465032196013458"
    ],
    [
      "921248768118",
      "68566127545385158"
    ],
    [
      "1513488732693",
      "1024167210723639748"
    ],
    [
      "1302979350498",
      "-614330875561576877"
    ],
    [
      "983923487169",
      "-41724359928135728"
    ],
    [
      "976260793788",
      "29802115059241003"
    ],
    [
      "444611621769",
      "794507147074906408"
    ],
    [
      "1194706365594",
      "-412870946793845453"
    ],
    [
      "472461354918",
      "-756080230805621117"
    ],
    [
      "957288103968",
      "-15852600561045077"
    ],
    [
      "441115178406",
      "799294168677977731"
    ],
    [
      "2456535768288",
      "-3129456458737080917"
    ],
    [
      "1134305072523",
      "303349975608016648"
    ],
    [
      "1175405086086",
      "377645080063855222"
    ],
    [
      "982431954861",
      "-39342857401778228"
    ],
    [
      "1401568389501",
      "-803340781131078404"
    ],
    [
      "3567736384359/4",
      "933938344059977861/8"
    ],
    [
      "7999856558043",
      "-22171701369808730492"
    ]
  ],
  "submitter": "RoyManami",
  "commentary": "Rank-19 height AND conductor record: h=180.457 (beats 190.312), log N=142.954 (beats 146.224). New 3-parameter sub-family of Mestre locus 12*p5=5*p2*p3: six roots = union of two depth-2 cubics x^3+px+q, x^3+rx+s with (p-r)(q-s)=0 (equal product), disjoint from Mestre (u,v) slice. Sextuple {0,203,204,254,370,523}, T=1303/3; base-point injection + Neron-Tate independence (19 indep).",
  "created_at": "2026-06-26 01:21:18",
  "updated_at": "2026-07-01 22:30:41"
}