curve #345

y² + xy = x³ − 484958388528014875755905011x + 3744479970311738957262814782831867617210

a-invariants: [1, 0, 0, -484958388528014875755905011, 3744479970311738957262814782831867617210]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 15587568597617774467402317716515315920379328015617095707375221511102745
naive height: 195.9519
Faltings height: 14.2974
discriminant (Δ): 1242376586837912826623415817268660517325818940797865667216548646753671619520376575
primes of bad reduction: 3, 5, 13, 17, 43, 59, 4957, 112680298688013869, 556778714430176039, 350570948823095172152501
regulator: 1791167772689157304223.611019527105214873682087862686091484303980899842195464
submitted by: Christopher R. Hill
submitted at: 2026-08-25 01:51:19 UTC
last updated: 2026-08-25 02:23:48 UTC

(-101791341984043097/6241, -42169668028186974383448836/493039)
(3591783271004041/2209, -5648818149132898530244360/103823)
(22664766398921638, -3412138628304175859626214)
(7838223611066374/1089, -899723019021596131359190/35937)
(2704011059006677/144, 61318917500151209301353/1728)
(7509774080558, 22936398763978883726)
(3255660216531480652013/49014001, -176509781229836808564333129687464/343147021001)
(1934273239604399785979/37662769, -78143223537438053882304294322460/231136413353)
(27097107906727960241/5161984, 429862079163436833922174015865/11728027648)
(53157468617172969089/3385600, -5547766048575169911065244343/6229504000)
(34889287938698114918/3682561, -3855530418535743739341789626/7066834559)
(-49304657155409122/3481, 18105848993468105624759644/205379)
(1049443481558, -56891997641493955774)
(360814935600809/49, 8208552641946584083640/343)
(-1364906852124703/64, 33912365798984702720707/512)
(900834556517702/49, 11074555552417184584448/343)
(1815614187504105590/113569, 336802173476142362725524920/38272753)
(-43956697577661874/2209, -7710433102642523745764222/103823)
(122103918760307/4, 1054842869711431238383/8)

Found with Rank Hunter v0.7.21; family=Mestre/Fermigier sextuple, generic rank >=11; parameter=9736/9; local status: rigorous rank lower bound >= 19.

last edited by Christopher R. Hill at 2026-08-25 02:28:19 UTC · history