{
  "id": 6175,
  "curve_key": "962006304595909134943201:-942658734626350859724046214304026449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-20041798012414773644650",
    "1091040202112161863735130035418532"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 165.6699238714596,
  "faltings_height": 11.577350239317784,
  "conductor": "4111423344469783039462650315957622792007824170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "1151659200131591887804663954049754283475581"
  ],
  "discriminant": "977512615005441240448081346977350672230303316160000170424320000000",
  "regulator": "503112787770038352205.914050451455772934315842224602834646652385911571998",
  "points": [
    [
      "86912368454",
      "2382229174010048"
    ],
    [
      "89068018804",
      "3541639574358598"
    ],
    [
      "-260368456797376556/1907161",
      "94327824796376019426055918/2633789341"
    ],
    [
      "-3202343404488296/19881",
      "33183062327308914577598/2803221"
    ],
    [
      "36709256155924/841",
      "421999477512282878942/24389"
    ],
    [
      "1227025726597364/14641",
      "284009273083410703478/1771561"
    ],
    [
      "1769818078512212/52441",
      "255623109454659054360302/12008989"
    ],
    [
      "3300202899464684/3481",
      "187585038784538133115762/205379"
    ],
    [
      "11704096499525924/3481",
      "1265108162349029153463442/205379"
    ],
    [
      "24796523094621524/502681",
      "5315490150974115903085742/356400829"
    ],
    [
      "100323595040580724/1985281",
      "40274621514272410860451142/2797260929"
    ],
    [
      "329675891238309956/4338889",
      "23722157313774398512985426/9037905787"
    ],
    [
      "1163865422333886644/1907161",
      "1224449167439307035889439118/2633789341"
    ],
    [
      "9904451274376521886/115627009",
      "2080058293416924976106894746/1243337227777"
    ],
    [
      "10817821672974115724/129026881",
      "362245046690878226591443442/1465616341279"
    ],
    [
      "13813295670219982196/179372449",
      "5001409156411887626632746086/2402335209457"
    ],
    [
      "711604499283390482834/10520399761",
      "7228476136182485085634549388692/1079066883086009"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,9,31,43,80,81,83,104,110,129: 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 14:40:11",
  "updated_at": "2026-10-30 14:40:11"
}