{
  "id": 6176,
  "curve_key": "847071887440336579281:-24537611654685371368821374318745",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-17647330988340345402",
    "28400013493631012572109825145"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 144.56495171386317,
  "faltings_height": 9.88042511766856,
  "conductor": "4190506510606183610086555829247330835129764106",
  "bad_primes": [
    "2",
    "7",
    "59",
    "97",
    "521",
    "14083",
    "3773701",
    "5545081",
    "7089637",
    "48048789943163"
  ],
  "discriminant": "3301949366703454340468160175261458814790094726110976950272",
  "regulator": "788195472308523695.768949439230876569887105436989149043139828192830290140",
  "points": [
    [
      "-706103897",
      "201268362131617"
    ],
    [
      "2560486745",
      "1020494782255"
    ],
    [
      "16955937745",
      "2145701176816999"
    ],
    [
      "-7272095770055/1521",
      "3500198972727312881/59319"
    ],
    [
      "24516485377/81",
      "110765621113039855/729"
    ],
    [
      "101390728249/25",
      "19176754830707547/125"
    ],
    [
      "207998312353/81",
      "2951875900739791/729"
    ],
    [
      "619670339217/361",
      "385899286293705845/6859"
    ],
    [
      "707039513001/625",
      "1553400532327585799/15625"
    ],
    [
      "965222372929/289",
      "402605251136938503/4913"
    ],
    [
      "1578612518161/729",
      "362794850113251725/19683"
    ],
    [
      "8028137751649/3136",
      "38200376536399755/175616"
    ],
    [
      "16128680761945/4489",
      "32078524500597224605/300763"
    ],
    [
      "24924759490629/6889",
      "62406149722163978209/571787"
    ],
    [
      "80358020274297/72361",
      "1963160479643315294163/19465109"
    ],
    [
      "146565135739153/9409",
      "1715537196854497472935/912673"
    ],
    [
      "3724011707395341/638401",
      "179583303428908210664333/510082399"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,11,55,69,83,93,94,97,108,124: 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 17, proved: 17 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-30 14:40:19",
  "updated_at": "2026-10-30 14:40:19"
}