{
  "id": 1384,
  "curve_key": "65226569662542736:-16658532985591304575029440",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-1358886867969640",
    "19280709927026299248016"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "naive_height": 116.14992987298582,
  "faltings_height": 7.200498044209567,
  "conductor": "134794654972773356297689104",
  "bad_primes": [
    "2",
    "3",
    "17",
    "29",
    "37",
    "41",
    "53",
    "73",
    "101",
    "109",
    "223",
    "13327",
    "29663"
  ],
  "discriminant": "41067544627117908429577324461210976561152",
  "regulator": "17980304983.7402146072907109074406501765054753460153535786501",
  "points": [
    [
      "21290386",
      "-33206706"
    ],
    [
      "21297433",
      "104893488"
    ],
    [
      "21611938",
      "-2635400718"
    ],
    [
      "21343261",
      "479894706"
    ],
    [
      "21293858",
      "72023538"
    ],
    [
      "21313946",
      "243025986"
    ],
    [
      "21429578",
      "-1172242242"
    ],
    [
      "23428786",
      "-17432387406"
    ],
    [
      "21321641",
      "-305559204"
    ],
    [
      "21390941",
      "862519554"
    ],
    [
      "532539946/25",
      "17605466694/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "2-isogenous quotient of curve #1381, submitted by N. D. Elkies. Translating the rational 2-torsion point of #1381 to \\((0,0)\\) gives \\(y^2=x^3-31915045x^2+254840875546408x\\); quotienting by \\((0,0)\\) gives this curve. The 11 witness points are the explicit Vélu images of the 11 independent points on #1381. It has the same conductor and torsion \\(Z/2Z\\), while its minimal discriminant is \\(41067544627117908429577324461210976561152\\), smaller in absolute value than #1381 by a factor of approximately 20.07494.",
  "created_at": "2026-09-24 20:19:41",
  "updated_at": "2026-09-24 20:19:41"
}