{
  "id": 6480,
  "curve_key": "613517073872976:-15138179922880838891160",
  "ainvs": [
    "0",
    "0",
    "1",
    "-12781605705687",
    "17521041577408378346"
  ],
  "rank_lower_bound": 14,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 102.15068762989817,
  "faltings_height": 6.337529082464546,
  "conductor": "155339352465722439837472406302227",
  "bad_primes": [
    "3",
    "11",
    "61",
    "419",
    "61390679147878661349388247"
  ],
  "discriminant": "1021584746649602119640381993346813100917",
  "regulator": "43923218976.5604185270230936023729307766716167676869965794918791191",
  "points": [
    [
      "73675452/49",
      "447492590203/343"
    ],
    [
      "463581891",
      "-9981063464576"
    ],
    [
      "204606282/169",
      "4294609065391/2197"
    ],
    [
      "3195528334/289",
      "-172169705006033/4913"
    ],
    [
      "8670993/4",
      "-132514573/8"
    ],
    [
      "2096450676/961",
      "4175700410875/29791"
    ],
    [
      "25571086/9",
      "54947880917/27"
    ],
    [
      "1480481916/169",
      "52811670496801/2197"
    ],
    [
      "164790452553/9409",
      "65598463689203515/912673"
    ],
    [
      "1882977",
      "360360580"
    ],
    [
      "1950138",
      "107684428"
    ],
    [
      "1955682",
      "64551019"
    ],
    [
      "9169548",
      "25909471021"
    ],
    [
      "18664077",
      "79249944955"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,14,26,34,60,62,66,78,97,113: with p(x) = prod (x - a_i), write p = q^2 - r with q a monic quintic and deg r <= 4; the genus-one curve y^2 = r(x) carries the ten points (a_i, q(a_i)), and the curve submitted is the minimal Weierstrass model of its Jacobian. Found by enumerating integer ten-root sets 0 = a_1 < ... < a_10 and scoring each by S = sum of -a_p log(p)/p over the good primes 5 <= p <= 199 (with early abort on low partial sums); the sets with S >= 31, or S >= 30 and one bad prime in that range, or S >= 29 and two or more bad primes, were screened by exact conductor and by a GRH explicit-formula upper bound on the rank, and the survivors were certified with ellrank. Rank 14, proved: 14 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-11-04 02:11:45",
  "updated_at": "2026-11-04 02:11:45"
}