curve #1214

y² + xy = x³ − 326034514850898538462143577535732108974101688866x + 126139807177463916084745782524191445068029238338478785879968870214064452

a-invariants: [1, 0, 0, -326034514850898538462143577535732108974101688866, 126139807177463916084745782524191445068029238338478785879968870214064452]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/7ℤ
conductor (N): 208438088888422834748960003426893818 ☆ record for ℤ/7ℤ torsion, rank ≥ 6
discriminant (Δ): -4655613598636301869576831935534516912675653961862170243923410997485709643437217760687425229920490939729066863282310721116318099588791147203395584 ☆ record for ℤ/7ℤ torsion, rank ≥ 6
Faltings height: 26.4529 ☆ record for ℤ/7ℤ torsion, rank ≥ 6
naive height: 340.9547 ☆ record for ℤ/7ℤ torsion, rank ≥ 6
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 23, 29, 41, 73, 83, 107, 883, 13259, 517634646983
regulator: 16451305.350998580257497630998695850867104196098600
submitted by: dujella
submitted at: 2026-09-24 14:08:39 UTC
last updated: 2026-09-24 14:08:39 UTC

(349621108430722643628612, 234280103165415296096052964651107726)
(408970490120129839927524, 247395296205394205764203536688391182)
(-394276731764242099773348, -439767756206926097966811118650051474)
(15487208600555969620583619/4, 60348540330823105469521400748864009759/8)
(488457152640052085194896, 288837495697090305635327960027037486)
(6109083865034034966377150522923236/6323271361, 424558236702135759868877367327409557236105861623602/502820215355359)

found by Klagsbrun (2020)

last edited by dujella at 2026-09-24 14:08:39 UTC · history