{
  "id": 4994,
  "curve_key": "-15152270784:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "315672308",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 70.32424873320771,
  "faltings_height": 3.9285944727421325,
  "conductor": "4067306368899872",
  "bad_primes": [
    "2",
    "7",
    "19",
    "29",
    "37",
    "79"
  ],
  "discriminant": "-2013211630459916119746695168",
  "regulator": "1234.12170754437686570019756369074145476388116797",
  "points": [
    [
      "406",
      "358092"
    ],
    [
      "1862",
      "770868"
    ],
    [
      "12950",
      "2501940"
    ],
    [
      "19684",
      "3720276"
    ],
    [
      "20461/9",
      "23059547/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #4993: https://elliptic-rank.icarm.cloud/curve/4993. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (14,28,32,34), reduced by rational fourth-power scaling. Reference: \"High rank elliptic curves with torsion group Z/(2Z)\", Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Points transported by the rational 2-isogeny and reduced with PARI/GP. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 01:35:26",
  "updated_at": "2026-10-21 01:35:26"
}