{
  "id": 6017,
  "curve_key": "24219897418846261521:-125088152515327124136525236985",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-504581196225963782",
    "144777954426292433473765525"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 133.99763243942658,
  "faltings_height": 9.102394546419756,
  "conductor": "3877468398357428055736663961087371709872782",
  "bad_primes": [
    "2",
    "3",
    "7",
    "59",
    "14029",
    "37179110483154681871811441827026887"
  ],
  "discriminant": "-833085055458646556236758693317513896880810837416869888",
  "regulator": "6367756631810670.921758079272559177658031554567260139245615520801682741",
  "points": [
    [
      "-207334007",
      "15507587271707"
    ],
    [
      "-135065783",
      "14507501328347"
    ],
    [
      "-89028407",
      "13747566846299"
    ],
    [
      "182349385",
      "7670061194459"
    ],
    [
      "285994889",
      "4884804597275"
    ],
    [
      "286180889",
      "4879870344635"
    ],
    [
      "508811017",
      "4445741595035"
    ],
    [
      "604970633",
      "7805722615067"
    ],
    [
      "3147861193",
      "172476475868507"
    ],
    [
      "4290516553",
      "277418071163099"
    ],
    [
      "-5051347191782975/7689529",
      "296055000292432351459775/21323063917"
    ],
    [
      "-4694004863/9",
      "440422700916073/27"
    ],
    [
      "31051353649/169",
      "16770698746768247/2197"
    ],
    [
      "2095655210413/6561",
      "2138697620161129747/531441"
    ],
    [
      "7665111831091/19881",
      "7701047309500862351/2803221"
    ],
    [
      "221062089789421/657721",
      "1934557999764212302997/533411731"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,3,19,22,38,47,49,51,53,72: 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 the sum of -a_p log(p)/p over 5 <= p <= 199 (with early abort on low partial sums); the sets scoring at least 31 were screened by exact conductor and by a GRH explicit-formula upper bound on the rank, and the survivors were certified with ellrank. Rank 16, proved: 16 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-28 06:03:50",
  "updated_at": "2026-10-28 06:03:50"
}