{
  "id": 6396,
  "curve_key": "584966046590896516033164513984:-444659504130556117469811909862658466482276352",
  "ainvs": [
    "0",
    "0",
    "0",
    "-12186792637310344084024260708",
    "514652203854810321145615636415113965835968"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 205.62405394911343,
  "faltings_height": 14.97961242195123,
  "conductor": "79295595036121358250617842517352625894080",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "37",
    "43",
    "61",
    "89",
    "151",
    "163",
    "173",
    "179",
    "263",
    "443",
    "479",
    "859",
    "1663",
    "12197"
  ],
  "discriminant": "1414753063229824692904474740434030911760271367703886547083533970799476536860285440000",
  "regulator": "4874422901.46907885639576714447371141468216109933214071214869",
  "points": [
    [
      "52062025402461",
      "145927538372663116569"
    ],
    [
      "2252746958713129/16",
      "80698502119676560066475/64"
    ],
    [
      "58190764672194",
      "50368218789774146400"
    ],
    [
      "44641574795712589/625",
      "1448337472624310305557313/15625"
    ],
    [
      "104263297876794",
      "614366462584492479000"
    ],
    [
      "58937640177594",
      "33464442599163714600"
    ],
    [
      "36520155928806",
      "343942384957838742456"
    ],
    [
      "-126127430690622",
      "212813623559043216864"
    ],
    [
      "166613843530857/4",
      "2252810768239220196843/8"
    ],
    [
      "-27772451761956",
      "-911969391140150440500"
    ],
    [
      "176717613287577372/1369",
      "52942979478598899026977332/50653"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=1916/575. Family equations as posted by wgxli with curve #4252; section formulas from the Layr Labs Elliptic Rank Challenge repository (submission/research/x400a-family.gp, commit 7482bf9). T selected by our Mestre-Nagao sieve; PARI/GP 2.19 ellrank seeded with the family sections, bounds [11,11]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 01:17:08",
  "updated_at": "2026-11-02 01:17:08"
}